BULLETIN  G.  w.  B.  NO.  221. 

U.'S.  DEPARTMENT   OF   AGRICULTURE. 

WEATHER     BUREAU. 


ATMOSPHERIC  RADIATION: 


A  RESEARCH 


AT  PROVIDENCE,  R.  I. 


SUBMITTED  TO  'WILLIS  L.  MOORE,  CHIEF  U.  S.  WEATHER  BUREAU, 

BY 

FRANK   W.  VERY. 

h 


WASHINGTON: 

GOVERNMENT     PRINTING     OFFICE. 
1900. 


V 

PHYSICS  DEFT, 


PHYSICS  DEPT. 


LETTER  OF  TRANSMITTAL. 


UNITED  STATES  DEPARTMENT  OF  AGRICULTURE, 

WEATHER  BUREAU, 

«  Washington,  D.  0.,  January  4, 1900. 

Hon.  JAMES  WILSON, 

Secretary  of  Agriculture. 

SIR:  I  have  the  honor  herewith  to  transmit  for  publication,  as  a  bulletin  of  the  Weather 
Bureau,  a  memoir  by  Prof.  Frank  W.  Very  on  "Atmospheric  Kadiatiou." 

This  paper  gives  the  results  of  a  long  research  carried  on  by  Professor  Very  during  the  past 
eight  years.  The  expense  of  the  apparatus  was  defrayed  by  Prof.  James  E.  Keeler,  Director  of  the 
Allegheny  Observatory,  from  funds  allotted  for  this  purpose  by  the  Hon.  J.  M.  Eusk  on  the 
recommendation  of  my  predecessor. 

An  examination  of  the  manuscript  will  show  that  Professor  Very  has  brought  to  bear  upon 
the  study  of  this  important  subject  a  wide  range  of  knowledge  and  experimental  skill  acquired 
by  his  long  service  in  connection  with  Prof.  S.  P.  Laugley  in  researches  on  radiation  at  the  Alle- 
gheny Observatory.  Professor  Very  has  attacked  a  problem  that  has  long  been  recognized  as 
being  of  fundamental  importance  in  climatology  and  general  meteorology.  He  has  apparently 
settled  some  questions  that  have  heretofore  been  under  discussion,  but  has  also  raised  others  for 
future  investigators  to  discuss. 

This  memoir  is,  therefore,  to  be  recognized  as  one  step  of  progress  in  our  knowledge  of  the 
subject  of  radiation  and  absorption  of  heat  by  the  earth's  atmosphere,  and  I  take  great  pleasure 
in  commending  it  to  you. 

Very  respectfully,  your  obedient  servant, 

WILLIS  L.  MOORE, 

Approved :  Chief  United  States  Weather  Bureau. 

JAMES  WILSON, 

Secretary  of  Agriculture. 

3 


810833 


ATMOSPHERIC    RADIATION 


By  FRANK  W.  VERY. 


PREFATORY  NOTE. 

This  research  was  first  suggested  in  a  letter  from  Prof.  Cleveland  Abbe,  of  the  United  States 
Weather  Bureau,  to  the  writer,  dated  November  24,  3891,  in  the  course  of  which  he  said: 

Absorption  may  be  the  absolute  inverse  of  radiation  for  gases,  but  I  don't  like  to  assume  this  as  to  intensity,  and  so 
I  beg  to  know  whether  you  and  Professor  Keelercau  not  undertake  the  following  problem :  To  determine  the  absolute 
radiation  in  calories  from  a  unit  mass  of  gas  at  given  density  and  temperature  and  at  ordinary  temperatures,  not 
when  burning,  nor  when  electrified,  but  when  simply  heated. 

Maurerhas  given  the  only  determination  that  I  know  of,  but  this  is  only  computed  from  meteorological  observa- 
tions of  cooling  at  night,  and  his  figures  demand  continuation  by  direct  experiment.  He  finds 

6  =  coefficient  of  radiation  for  air,  or  the  amount  of  heat  in  calories  that  one  unit  volume  of  air 

[at  the  level  of  the  station  where  6  =  29.5  inches;  temperature  =  40°?  Fahr.]  loses  by  radiation  in  unit  time 
(one  hour)  to  a  surrounding  surface  of  air  whose  temperature  is  1°  lower  —  0.0000418  gram  calories  per  cubic 
centimeter  per  hour.  And  again  from  direct  radiation  observations,  he  finds  0.000039  calories. 

It  ought  to  be  possible  to  determine  the  quantity  and  quality  of  the  heat  radiated  by  a  mass  of  warm 
gas.  *  The  stream  of  gas  should  be  varied  as  to  its  diameter,  so  sis  to  determine  the  effect  of  depth  from 

which  radiation  comes.  The  ascending  flow  of  warm  gas  can  be  kept  steady  for  any  length  of  time  or  cut  off  at 
will.  The  black  surface  that  serves  as  the  basis  for  reference  should  be  surrounded  by  a  screen  at  0°C.,  so  that  it 
can  only  receive  and  transmit  or  reflect  the  waves  that  belong  thereto. 

In  regard  to  the  direct  measurement  of  gaseous  radiations  of  nearly  homogeneous  quality  at 
moderate  temperatures,  the  following  was  written  in  reply  (November  27,  1891): 

The  problem  which  you  suggest  is  an  exceedingly  difficult  one.  I  should  anticipate  that  the  radiation  from  so 
small  a  mass  of  gas  as  that  in  a  transverse  jet  would  be  almost  immeasurable,  unless  at  very  high  temperature. 
Possibly  two  long,  diaphragmed  tubes,  surrounded  by  water  jackets,  and  open  at  both  ends,  would  answer  for 
ordinary  temperatures  when  interposed  in  alternation;  e.  g.  let  temperature  of  room  be  +  20°C.,  one  tube  being 
surrounded  by  a  freezing  mixture  at  — 20CC.,  and  the  other  by  warm  water  at  +60°C.  The  temperature  gradients 
in  the  open  tubes  would  be  similar  and  are  also  determiuable. 

In  commenting  on  the  above  suggestion,  Professor  Abbe  expressed  the  hope  that  temperatures 
as  low  as  —90°  C.  might  be  attained,  but  added  further  the  important  remark  that  "the  point  to 
be  determined  experimentally  is  the  law  of  radiation,  transmission,  and  absorption  as  depending 
upon  pressure  or  density  of  the  air  rather  than  as  depending  upon  temperature." 

By  the  advice  and  consent  of  Professor  Keeler,  Director  of  the  Allegheny  Observatory, 
preliminary  experiments  were  commenced  in  March,  1892,  with  an  apparatus  similar  to  that  out- 
lined in  the  writer's  letter  of  November  27,  1891;  but  as  entire  confidence  could  not  be  placed  in 
any  one  method,  and  as  the  complete  accomplishment  of  the  work  contemplated  required  measure- 
ments of  atmospheric  radiation  at  various  pressures,  a  more  elaborate  apparatus  was  devised 
with  which  experiments  were  begun  in  1894  and  continued  in  the  intervals  between  other  occupa- 
tions until  the  severing  of  my  connection  with  the  Observatory  in  1895.  The  reduction  of  the 
observations  begun  at  Allegheny  was  afterwards  continued  at  Providence,  R.  I.,  and  required  the 
further  consideration  of  a  number  of  obscure  and  troublesome  details  for  which  I  did  not  find  time 
for  several  years,  but  it  is  hoped  that  the  last  of  these  difficulties  has  now  been  successfully  met. 

5 


6 

The  problem  has  proved  much  more  extensive  than  I  imagined  when  I  first  undertook  its 
solution.  It  is,  besides,  beset  with  difficulties.  Some  of  the  greatest  masters  of  science  have 
worked  at  it  with  only  partial  success,  and  with  merely  qualitative  results.  Professor  Tyndall 
rightly  emphasized  the  necessity  of  a  long  apprenticeship  in  the  methods  and  manipulations 
appropriate  to  this  study  before  one  can  be  ready  to  appreciate  the  subtle  sources  of  error  to 
which  this  particular  research  is  open.  The  investigator  here  is  dealing  with  the  invisible  and  the 
evanescent.  In  an  optical  apparatus,  a  little  stray  light  immediately  attracts  attention,  and  we 
proceed  to  trace  it  to  its  source  with  our  eyes  open.  In  our  study  of  feeble  invisible  radiations, 
on  the  other  hand,  we  grope  in  the  dark,  and  only  succeed  in  eliminating  the  unwelcome 
extraneous  rays  after  innumerable  trials  and  errors. 

The  final  apparatus  for  work  at  various  pressures  frequently  gave  trouble  by  springing  leaks 
when  heated  j  and  the  possibility  of  contamination  of  the  air  column  by  evaporation  or  combus- 
tion of  organic  substances  prevented  the  employment  of  elevated  temperatures.  Moreover,  it 
was  especially  desired  that  the  temperatures  should  not  greatly  exceed  those  of  the  ordinary 
atmospheric  range.  Hence  the  radiations  measured  have  been  of  small  magnitude,  requiring  a 
sensitive  measuring  apparatus,  and  attention  to  many  minute  details  inevitable  in  measurements 
of  this  character.  I  shall  not  trouble  the  reader  with  a  recital  of  all  the  difficulties  encountered; 
but,  in  order  that  the  meaning  and  value  of  the  results  may  be  quite  clear,  it  will  be  necessary  to 
consider  the  theory  of  some  parts  of  the  apparatus  carefully. 


MEASURING  INSTRUMENTS. 
THE  BOLOMETER. 

The  measurements  of  radiation  have  all  been  made  with  a  bolometer  constructed  after  Lang- 
ley's  earlier  plans,  in  which  the  exposed  face  is  composed  of  very  thin  strips  of  blackened  platinum, 
arranged  in  two  series,  those  in  the  rear  occupying  the  positions  of  the  apertures  in  the  front 
series.  The  unexposed  member  is  of  nearly  identical  resistance  and  is  divided  into  two  parts,  one 
on  each  side  of  the  central  member,  which  receives  the  radiation  coining  through  the  graduated 
apertures  of  the  bolometer  case.  The  electric  current  passes  to  and  fro  along  the  strips  which  are 
held  separate  and  insulated  by  grooves  in  the  disk  of  an  ebonite  holder,  a  disposition  which  is 
objectionable,  as  I  shall  show  presently,  but  which  does  not  prevent  the  instrument  from  being 
used  for  certain  classes  of  relative  measurements,  where  the  accompanying  conditions  do  not 
vary  much. 

The  bolometer  battery  consisted  of  eight  gravity  cells  arranged  in  one  series,  the  current 
being  reduced  to  its  working  strength  by  interposing  resistance  between  the  battery  and  the 
Wheatstone's  bridge,  of  which  the  bolometer  forms  a  part. 

When  a  bolometer  of  two  nearly  equal  arms  is  used,  it  is  desirable,  in  order  to  secure  the 
most  sensitive  combination,  that  the  balancing  arms  of  the  Wheatstone's  bridge  should  be  of 
greater  resistance  than  the  bolometer  arms,  in  case  all  of  the  resistances  can  not  be  made  equal. 
Since  in  the  bridge  used  by  me,  choice  could  be  made  between  balancing  resistances  of  1,  10,  or 
100  ohms,  the  bolometer  arms  being  a  little  over  31.5  ohms,  at  20°  C.,  or  with  connections  about 
32  ohms  in  all,  the  normal  arrangement  of  the  bridge  is  with  balancing  arms  of  100  ohms.  But 
on  several  occasions  the  bridge,  being  used  for  different  purposes,  was  inadvertently  left  with 
balancing  arms  of  only  10  ohms.  It  becomes  necessary,  therefore,  to  reduce  these  measures  to 
normal  sensitiveness  of  a  100  :  32  bridge. 

According  to  theory,  the  current  through  the  galvanometer  is,  by  Kirchhoff's  law: 

C  =  E-(r*r*~r^ 
where 

D  =  r5r6  (r{  +  rt  +  r.}  +  r4)  +  r5  (rt  -f  r;j)  (r.z  +  r4)  +  rti  (r{  -f  rt)  (r3  +  r,)  +  r^  (r2  -f  r4)  +  r2r4  (r,  -f  r3). 


In  the  normal  arrangement  (1),  and  the  exceptional   or  insensitive   arrangement  (2),  the 
currents  in  consecutive  experiments  were  : 


Measured  battery  current  =  0.026  ampere. 
"  "    '        "        =0.032        " 


(1) 

(2) 

The  extra  resistance  (-K),  plus  that  of  the  bridge,  was: 

(1)  R  +  %  (r,   +  r3)  =  266  ohms. 

(2)  JR  +  £(r'1+r3)=221      « 

Assuming  the  electromotive  force  of  one  gravity  cell  to  be  1.1  volt,  the  total  resistance  of 
eight  cells,  plus  an  extra  resistance  of  200  ohms,  plus  the  bridge,  should  have  been  : 


(1) 


>-6  +  -R  + 


+  r3)  = 


=  338.5  ohms. 


whence  the  apparent  resistance  of  the  battery  was: 


(1) 

(2) 


For  eight  cells,  72.5  ohms;  for  one  cell,  9.2  ohms. 
"        "         "       54.0     "         ;<      "       "     6.9     " 


According  to  this,  the  diminution  of  the  external  resistance  from  266  to  221,  or  by  17  per 
cent.,  increased  the  current  by  23  per  cent.,  the  battery  resistance  at  the  same  time  diminishing  by 
25  per  cent.  It  is  possible  that  a  portion  of  the  change  was  in  the  potential  of  the  battery,  and 
both  voltage  and  resistance  may  have  been  lower  than  the  values  given;  but  for  the  purposes  of 
a  test,  the  resistances  may  be  taken  as  stated,  and  assuming  further  that  the  exposed  arm  of  the 
bolometer  has  its  resistance  increased  by  radiation  by  0,005  ohm,  I  proceed  to  calculate  the  current 
through  the  galvanometer  in  each  of  the  two  arrangements  of  the  bridge.  The  resistances  at 
20°C.  are  those  of  the  Elliott  coils,  graduated  according  to  British  Association  units,  of  which 
1  =  0.989  of  the  the  accepted  legal  ohm. 

(1)  n  =  r2  =  100,        r3  =  32.005,         »-4  =  32,        r5  =  20.5,        r6  =  272.5.* 

(2)  r'i  =  r'2=    10,         r3  =  32.005,         r4  =  32,         r5  =  20.5,         r'6  =  254. 

D  „  =  (20.5  x  272.5  x  264.005)  +  (20.5  x  132.005  x  132)  +  (272.5  x  200  x  64.005) 

+  (100  x  32.005  x  132)  +  (100  x  32  x  132.005)  =  6  165  159. 

D;2)  =  (20.5  x  254  x  84.005)  +  (20.5  x  42.005  x  42)  +  (254  x  20  x  64.005)  +  (10  x  32.005  x  42) 
+  (10  x  32  x  42.005)  =  825  609. 


Computed  ratio  of  galvanometer  currents: 


5(2) 


=  1.339  + 


The'  theory  was  tested  by  exposing  the  bolometer  to  radiation  from  blackened  screens 
containing  boiling  water,  and  water  at  the  temperature  of  the  room  (about  30°  C.)  with  the 
followin  results: 


(1)     n  =  ra  =  100  ohms. 


(2)     r/1  =  r/2  =  10  ohms. 


Temperature  of  screens. 

Deflection 

Temperature  of  screens. 

Deflection. 

99°.  1 

366  div 

99°.  1 

232  div. 

29°.  4 

364 

30°.  2 

232 

0£T 

9Q9 

Excess,  69°.  7  C. 

OO  1 

367 

Excess,  68°.  9 

Ml>W 

235 

364 

233 

362 

231 

365 

231 

363 

230 

363 

230 

361 

230 

Mean  deflection 

=  364.2 

Mean  deflection 

=231.6 

>-6  is  supposed  to  include  the  extra  resistance  It. 


8 

Galvanometer  deflection  for  1°  of  temperature-excess  : 

(1)     5.225  div.  (2)     3.361  div. 

Ratio  of  observed  galvanometer  currents: 

^5   (l)  1     -r- 

r\    i   \  —  J..OOO 

^5   (2J 

To  bring  the  computed  value  into  agreement  with  theobser\ed,  a  battery  resistance  of  nearly 
1,000  ohms  would  be  required;  but  this  is  entirely  inadmissible,  since  any  bad  connection  would 
have  reduced  the  current  and  the  galvanometer  deflection,  both  of  -which  were  such  as  to  give 
customary  values  in  the  normal  reduction.  For  constant  battery  current  the  ratio  of  galvanometer 
currents  with  the  two  arrangements  should  be: 


C  (  }  0  03^ 

-~.   =  1.339  x  =  1-648  (computed) 


x  =1.913  (observed) 


Using  the  observed  factor,  observations  with  insensitive  condition  of  the  bridge  are  brought 
into  fair  agreement  with  normal  measures,  but  the  computed  factor  gives  discordant  results. 
There  can  be  no  doubt,  therefore,  of  the  substantial  accuracy  of  the  observed  ratio.  A  study  of 
these  discrepancies  has  elucidated  some  obscure  points  in  the  theory  of  the  bolometer,  which  I 
will  indicate. 

The  sensitiveness  of  a  bolometric  apparatus  is  a  complex  of  many  factors.  It  depends  upon 
the  resistance  of  the  bolometer,  the  material  of  its  strips,  and  the  rate  at  which  the  metal  varies 
in  resistance  with  changes  of  temperature,  the  absorbent  quality  of  the  surface  for  rays  of  various 
wave-lengths,  the  area  exposed  to  radiation,  the^  thickness  of  the  strips,  the  resistance  and  form 
of  the  galvanometer  coils,  the  strength  of  the  magnets  forming  the  needle,  the  ratio  of  their  mass 
to  the  other  parts  of  the  needle,  their  dimensions  and  position  in  reference  to  the  galvanometer 
coils,  the  astaticism  and  damping  of  the  needle,  the  torsion  of  its  suspending  fiber,  the  strength 
of  the  external  magnetic  field,  the  arrangement  of  the  Wheatstoue's  bridge,  the  strength  of  battery 
current  employed,  and  the  excess  to  which  the  bolometer  strips  are  heated  by  the  current.  The 
last  is  a  very  important  factor,  and  is  probably  responsible  for  the  greater  part  of  the  discrepancy 
between  incomplete  theory  and  observation  in  the  preceding  example.  The  theory  of  the  bolo- 
meter, in  fact,  can  not  be  reduced  to  a  simple  case  of  Wheatstone's  bridge,  unless  all  of  the  factors, 
with  the  exception  of  the  trifling  change  of  resistance  produced  by  the  radiation  to  be  measured, 
have  remained  constant. 

Prof.  Harry  F.  Eeid,  in  his  "Theory  of  the  bolometer"  (Am.  Journ.  of  Sci.,  ser.  3,  vol.  35,  p. 
160,  Feb.,  1888),  has  given  a  formula  for  the  bolometer  with  its  whole  surface  blackened  : 


in  which  6  is  the  galvanometer  deflection,  D  the  galvanometer  constant,  a  the  ratio  of  the 
resistance  of  the  bolometer  strips  at  the  temperature  t0  -\- 1°  to  their  resistance  at  temperature  /„, 
H  the  intensity  of  normal  radiation  per  unit  of  area  expressed  in  thermal  units,  a  the  relative 
absorbent  power,  of  the  bolometric  surface  exposed  to  radiation,  m  the  loss  of  heat  by  combined 
radiation  and  convection  (conduction  being  assumed  negligible)  in  thermal  units  for  the  unit  of 
time  and  unit  surface  of  the  strips,  i  the  ratio  of  the  resistance  of  the  exposed  part  of  the  strips 
to  the  entire  arm  of  the  Wheatstone's  bridge  of  which  they  form  a  part,  A  the  total  length  in 
series  of  the  exposed  part  of  the  bolometer  strips,  ft  the  width  of  an  individual  strip,  and  tl  —  t0 
the  excess  of  temperature  of  the  strips  due  to  the  battery  current  which  enters  as  the  square  root 
of  this  quantity,  the  current  being  here  stated  in  thermal  units,  and  the  galvanometer  constant 
also  having  reference  to  these  units.  The  formula  also  relates  to  the  most  efficient  arrangement 
of  the  bridge  resistances,  but  small  variations  from  this  ideal  are  of  minor  importance,  the  main 
point  being  that  the  bolometer  arms  shall  have,  as  nearly  as  possible,  equal  resistances,  and  be 
inclosed  in  a  common  chamber  which  can  be  kept  at  a  nearly  constant  temperature. 


9 


Professor  Reid  says  (p.  165-166) : 


Since  the  resistance  of  the  strip  does  not  enter  the  equation,  it  is  of  no  importance  so  long  as  the  fonr  arms  of 
the  bridge  and  the  galvanometer  all  have  the  same  resistance ;  but  this  should  not  be  so  small  as  to  decrease  materially 
the  value  of  i,  or  to  make  the  galvanometer  connections  an  appreciable  fraction  of  the  resistance  in  the  galvanometer 
branch.  /I  and  ft  only  occur  multiplied  together  and  under  the  radical  sign ;  other  things  being  equal,  S  varies  as  the 
square  root  of  the  exposable  area  of  the  strip.  For  a  given  area  it  does  not  matter,  then,  whether  the  strip  be  made 
of  a  single  broad  piece  of  platinum  or  of  several  narrow  pieces  arranged  side  by  side  and  connected  in  series.  This 
however,  is  subject  to  the  limitations  mentioned  in  regard  to  the  resistance  of  the  strip.  The  thickness  of  the 
strip  does  not  occur  in  the  expression  above;  we  have  supposed  the  strip  flat  and  so  thin  that  the  edges  are  only  a 
very  small  fraction  of  the  surface  and  the  heat  lost  by  conduction  negligible.  As  long  as  these  are  true  the  actual 
thickness  of  the  strip  is  unimportant,  (ti  —  t0)  is  the  increase  in  the  temperature  of  the  strip  above  the  case  due 
to  the  current  passing  through  it ;  for  a  particular  bolometer  it  is  proportional  to  the  square  of  the  current. 

The  equation  is  not  of  general  applicability,  and  some  of  the  assumptions  made  in  deducing 
it  are  not  warranted  by  facts  of  observation.  Thus  experiments  which  I  have  made,  some  of 
which  will  be  described  presently,  prove  that  conduction  of  heat  can  not  be  neglected  in  platinum 
two  or  three  microns  thick,  such  as  is  used  in  bolometers.  Again,  the  relation  between  the  heat 
generated  by  the  current  and  the  temperature  of  the  strip,  deduced  "  according  to  Kewton's  law 
of  cooling,  which  is  sufficiently  accurrate  for  the  small  change  in  temperature  under  considera 
tion,"'  in  Professor  Reid's  estimation,  is  shown  by  observation  to  require  a  more  complex  expres- 
sion, the  loss  of  heat  from  thin  strips  being  largely  produced  by  convection,  which  is  not  nearly 
proportional  to  excess  of  temperature ,  even  though  this  be  small. 

In  the  derivation  of  the  above  equation  the  galvanometer  resistance  has  been  assumed  equal 
to  that  of  one  arm  of  the  bolometer;  but,  as  shown  by  Schwendler  (Phil.  Mar/.  (4), vol.  33,  p.  29, 1867), 
the  neglect  of  the  space  occupied  by  insulating  material  has  led  to  an  error  in  this  customary 
allowance,  and  Mr.  F.  A.  Laws  (Phys.  Rev.,  vol.  5,  p.  300, 1897)  shows  by  trials  of  various  windings 
that  in  a  properly  wound  galvanometer  the  galvanometer  resistance  should  be  more  nearly  one-half 
that  of  one  of  the  bridge  arms  if  the  maximum  deflection  is  required.  However,  we  are  not 
concerned  so  much  with  those  factors  which  influence  the  galvanometer  constant  as  with  those 
which  enter  into  the  variable  bolometric  effect. 

The  excess  of  temperature  (ti  — 10),  which  in  a  given  bolometer  depends  mainly  on  the  battery 
current,  varies  with  the  square  of  the  current  and  inversely  as  the  section  of  the  strip.  It  is 
therefore  a  function  of  ft,  the  breadth,  and  6,  the  thickness  of  the  strip.  But  if  tf  oc  V  A.  ft(t\  —  t0)y 

the  substitution  of  the  relation, ^  —  /„  ex—,  in  this  variable  relation  gives: 

#  oc  V  £ 

and  other  things  being  equal,  that  bolometer  which  is  subdivided  into  the  largest  number  of 
strips,  or  has  the  largest  ratio  between  A.  and  ft,  should  give  the  greatest  galvanometer  deflection. 
Possibly  this  might  actually  be  the  case  in  a  vacuum,  but  in  air  more  than  one  cause  interferes 
with  its  realization.  To  keep  the  thin  metal  strips  from  undesired  electric  communication  an 
ebonite  holder  with  interlocking  grooves  has  been  used  in  the  instrument  belonging  to  my  outfit. 
The  heat  retained  by  the  nonconducting  holder  and  by  impeded  convection  very  nearly  neutralizes 
any  gain  that  might  result  from  the  subdivision.  But  the  theory  does  not  yield  readily  to  pure 
mathematics,  and  I  proceed  to  experiments  which  throw  some  light  on  the  activities  in  play  in  a 
working  bolometer. 

The  measures  in  the  following  table  were  made  several  years  ago  by  Professor  Reid  and 
myself,  and  were  laid  aside  as  hopelessly  discrepant;  but  with  further  experience  I  am  able  to 
explain  the  discordances,  and  to  show  that  they  contain  the  key  to  a  fuller  theory  of  the  actual 
instrument.  The  experiments  were  made  on  a  nearly  constant  source  of  radiation  with  a  single 
bolometer,  varying  the  battery  current  and  the  aperture  in  order  to  get  some  knowledge  of  the 
connection  between  A.  x  ft  and  t\  —  t0.  The  quantity  (2  v)  is  the  battery  current,  given  first  as 
originally  read  in  divisions  of  the  arbitrary  scale  of  the  battery  galvanometer,  and  afterwards  in 
amperes  as  corrected  by  the  calibration  of  the  scale.  The  constant  of  this  galvanometer  is 
1  div.  =  0.000  33  amp.  near  100  div.  T  is  the  excess  of  temperature  of  the  radiator.  The  other 
symbols  are  as  already  defined.  The  seventh  column  gives  values  reduced  to  uniform  battery 
current  and  the  eighth  to  full  aperture. 


10 

TABLE  1. 


1 

2 

3 

4 

5 

c 

7 

8 

& 

.0335 

For  aper- 

{ 

A/3 

T 

2w 

s 

f 

lif 

ture  of  ii 

8fj.  mm. 

°C. 

div.       amp. 

div. 

,=0.  60 

8.64 

81.0 

60    =0.0214 

72.5 

0.  895 

1.383 

,=0.  60 

8.64 

81.7 

82    =0.0279 

85,2 

1.043 

1.234 

,=0.  60 

8.64 

83.7 

166    =0.0480 

157.9 

1.886 

1.301 

1.340 

,=0.  60 

8.64 

82.6 

180    =0.  0508 

176.4 

2.138 

1.388 

!=0.  60 

8.64 

81.5 

196    =0.  0537 

185.4 

2.275 

1.396 

.7=0.  38 

5.40 

81.1 

115.5=0.0366 

81.2 

1.001 

0.902 

1.  4251 

is=0.  38 

5.40 

80.4 

126    =0.0391 

92.2 

1.147 

0.972 

1.  536J 

*j=0.  25 

3.60 

79.9 

160    =0.  0467 

77.7 

0.972 

0.685 

1.6441 

3=0.  25 

3.60 

79.4 

173    =0.  0493 

98.4 

1.239 

0.832 

1.997/ 

The  exposed  parts  of  the  bolometer  strips  constitute  62.4  per  cent,  of  the  whole,  or  allowing 
for  the  resistance  of  the  connections,  60  per  cent,  of  the  total  resistance  of  the  bolometeric  arm 
of  the  Wheatstone's  bridge  is  exposed  in  condition  v  The  mean  currents  giving  unit  deflection 
per  degree  of  temperature-excess  are  given  in  the  second  column  of  the  next  table. 

TABLE  2. 


Exposed  part. 

Battery  cur- 
rents. 

Equally  effi- 
cient cur- 

t 

2» 

rents  =  2v  X  i 

Ampere. 

Ampere. 

i1==0.  60 

0.  0252 

0.  01512 

f2=0.  38 

0.  0353 

0.  01341 

i.,=0.  25 

0.  0434 

0.  01085 

When  the  aperture  of  the  inner  bolometer  chamber  is  reduced,  a  larger  battery  current  is 
required  to  give  a  constant  galvanometer  deflection,  but  a  current  which  is  smaller  than  the 
inverse  proportion  of  the  aperture.  The  smaller  exposed  area  is  therefore  more  efficient  for  the 
unit  of  battery  current,  and  the  reason  of  this  seems  to  be  because  the  central  part  of  the  strips, 
heated  by  radiation,  are  adjoined,  in  the  case  of  the  smaller  aperture,  by  larger  portions  of  free 
strips  at  a  slightly  lower  temperature,  into  which  the  heat  can  pass  by  conduction  to  be  dissipated 
through  a  larger  surface,  but  at  a  lower  excess  of  temperature.  One  might  hesitate  to  predict 
whether  the  larger  surface  or  the  lower  excess  would  have  the  predominating  influence,  although 
in  general  two  units  of  surface  radiate  less  than  one  unit  at  twice  the  excess  of  the  two,  and 
the  experiment  decides  in  favor  of  this  view,  for  the  losses  are  less  when  the  heat  is  distributed 
to  a  relatively  wider  area,  so  that  a  smaller  current  is  then  needed  to  produce  a  given  deflection. 

Let  «i  be  the  area  of  the  fully  exposed  bolometer  strips,  «2,  the  area  of  the  central  part  when 
the  aperture  of  the  bolometer  chamber  is  reduced,  and  Ha^  Ha2,  the  heat  received  from  radiation 
in  the  two  conditions.  Owing  to  the  slight  thermal  conductivity  of  the  ebonite  holder,  the  heat 
developed  by  the  current  in  the  covered  parts  of  the  bolometer  raises  the  temperature  of  the  ends 
of  the  strips  excessively,  the  heat  from  the  covered  ends  being  partly  dissipated  by  conduction  to 
the  freely  exposed  parts,  where  it  passes  off  by  radiation  and  convection.  The  distribution  of 
temperature  in  the  shielded  strip  is  therefore  something  like  the  curve  in  fig.  1,  the  ends  (e)  being 
at  a  higher  temperature  than  the  middle  (w),  and  the  flow  of.  heat  being  in  the  direction  of  the 
arrows. 


11 


If  c"  is  a  current  larger  than  c7,  the  excess  of  temperature  of  the  strips  at  the  ends  under 
these  respective  currents  will  be: 


while  unless  conduction  more  than  compensates  for  the  relatively  greater  loss  by  radiation  and 
convection  at  the  higher  excess,  the  corresponding  quantity  in  the  middle  of  the  strips  will  be: 


(2) 

and  in  any  case 

(ti  -  t0)e  >  (t,  -  t0)m  ,  (3) 

the  subscript  e  and  m  denoting  end  and  middle  positions. 

During  exposure  of  the  central  part  of  a  strip  to  radiation,  conduction  from  the  sides  in  that 
part  must  be  diminished  or  reversed.  Since  the  temperature-excess  imparted  by  u  given  quantity 
of  heat  is  smaller  when  the  initial  temperature  is  greater,  £>  —  .t{  must  be  less  at  the  ends  than  at 
the  center  of  the  strip,  and  less  at  the  middle  for  the  greater  current;  also  the  mean  t2  —  <i,  or  the 
mean  excess  of  temperature  produced  by  radiation  received,  must  be  less  for  the  fully  exposed 
than  for  the  centrally  exposed  strip;  consequently,  AL  and  A2  being  lengths  of  the  exposed  part  of 
the  strips  for  full  and  for  partial  exposure,  and  the  temperature  varying  symmetrically  in  the  two 
halves  of  a  strip, 


• 

For  the  currents  c'  and  c"  the  deflections  are  approximately: 


X  (a  a,  c1} 


(A  A  being  a  small  element  of  length,  a  the  coefficient  of  change  of  resistance  with  temperature) 

^V-^A) 

°'   -  X  (a  02  C') 

2  ^2 

^-'OMA)  m 

)  V> 


<J"2  ex  ^— '  -  x  (a  02  c7') 

in  which 


Observation  shows  that 

fi'i  4-  o  i  c'   <C  <572  4-  o2  c7  (9) 

(y//l  4.  «,  C"  <  <5»8  _L.  a,,  C"  (10) 

tf'i  4-  a,  c7  >  tf 7/!  4-  ot  c77  (11) 

<5'2     4-  «2   C'      <   <y/72  4-   «2  C"  (12) 

Hence,  within  specified  limits, 

^JL/  <  £L.  <  ^.  <  ^.i  (13) 


12 


Inequality  (11)  is  a  consequence  of  the  unequal  distribution-  of  the  temperature-excess 
developed  by  the  battery  current  in  the  strips,  and  the  law  of  increase  of  this  excess  at 
the  preponderant  ends,  given  by  (1).  Inequality  (12),  dealing  with  a  part  of  the  strips  where 
temperature  is  fairly  equable,  is  a  consequence,  as  will  be  shown  presently,  of  the  great 
influence  of  convection  in  cooling,  and  the  rapid  rate  at  which  convection  increases  with  the 
temperature-excess  in  masses  of  matter  of  the  form  and  temperature  considered  here.  Inequality 
(13)  expresses  the  fact,  which  has  been  demonstrated  in  the  experiment  already  given,  that 
bolometers  of  reduced  aperture  are  relatively  more  efficient. 

Bolometers  used  with  full  aperture,  if  of  the  same  general  construction,  are  as  a  rule  more 
efficient  per  unit  of  area  when  the  number  of  strips  and  the  total  area  are  smaller. 

Determinations  of  the  battery  current  required  to  produce  a  nearly  constant  deflection  on 
an  approximately  constant  source  of  radiation  with  three  different  bolometers,  constructed  with 
various  arrangements  of  strips,  but  all  having  grooved  ebonite  holders,  gave  me  the  results  in 
the  next  table. 

TABLE  3. 

(Deflections  similar.) 


Number  of  strips  in  each  arm                            n 

1 

5 

23 

Length  of  strips  exposed                                   A 

8.  5  mm. 

48.  0  ram. 

184.  0  mm. 

Resistance  of  bolometer                                  B 

9.  2  ohm. 

14.  7  ohm. 

82.  1  ohm. 

Fraction  of  resistance  exposed                        i 

0.38 

0.60 

0.63 

Area  exposed                                                   A/3 

1.62  sq.  mm. 

8.  64  sq.  mm. 

42.3  sq.  mm. 

Section  of  strips                                               /36 

0.  000209  sq.  mm. 

0.  000504  sq.  mm. 

0.  000322  sq.  mm. 

Thickness  of  strips                                              6 

0.  0011  mm. 

0.  0014  mm. 

0.  0028  mm. 

Battery  current  (2»)  giving  uniform") 

(150.  5  div. 

60.  0  div. 

13.0  div. 

•deflection                                          .     J 

|=0.  0447  amp. 

—0.  0214  amp. 

=0.  0055  amp. 

Deflection  (mean  of  10  observations)             S 

73.  4  div. 

72.  6  div. 

75.  8  div. 

Probable  error  of  1  observation 

^0.  63  per  cent. 

-4^0.  42  per  cent. 

-J-0.  28  per  cent. 

Excess    of   temperature   of   radiant]            ^ 

82°  C. 

80GC. 

78°  C. 

source 

s 

Deflection  per  degree                                       -T-F, 

0.  895  div. 

0.  908  div. 

0.  972  div. 

Heat  developed  by  battery-current,  computed!:       n  A  t 

2.71 

1.00 

as  proportional  to  (2v)'2  R 

Deflection   per   degree   per   sq.  mm.  exposed! 

0.  552  div. 

0.  105  div. 

0.  023  div. 

area                                                                      J 

Deflection  per  degree  per  mm.  of  A 

0.  1053  div. 

0.  0189  div. 

0.  0053  div. 

Ratio  of  efficiency  per  mm.  of  A 

19.9 

3.6 

1.0 

Ratio  of  efficiency  per  sq.  mm.  of  A/?                       24.  0 

4.6 

1.0 

Ditto,  computed  for  constant  current  on  erro-\       «  034 
neous  assumption  S  oc  2v                                  J 

1.176 

1.000 

In  the  next  table,  further  measures,  made  with  the  same  bolometers  by  Professor  Reid  and 
myself,  give  a  comparison  of  deflections  on  a  nearly  constant  source  of  radiation  with  approxi- 
mately constant  battery  current. 

TABLE  4. 

(Currents  similar.) 


Number  of  strips  in  each  arm       •                     n 

1 

5 

23 

Length  of  strips  exposed                                    A 

8.5  mm. 

48.  0  mm. 

184.  0  mm. 

Battery  current                                                 2  v 

168.  0  div. 

166.  0  div. 

157.  5  div. 

Deflection  (mean  of  7,  16  and  10  obser-1 

91.  0  div. 

157.  9  div. 

327.  2  div. 

vations)                                                  J 

Probable  error  of  one  observation 

^0.  85  per  cent. 

-j-0.  44  per  cent. 

^0.  33  per  cent. 

Excess   of   temperature    of   radiant!            ™ 
source                                                     J 

75°.  5C. 

83°.  7  C. 

78C'.  4C. 

Deflection  per  degree 

1.205  div. 

1.  886  <liv. 

4.  173  div. 

Heat  developed  by  battery  current,! 

1    00 

1.  56 

7.85 

computed  as  proportional  to  (2v)'2  B  \ 

X.  \J\J 

Deflection  per  degree  per  sq.  mm.  ex-1 

0.  744  div. 

0.  218  div. 

0.  099  div. 

posed  area                                             J 

Deflection  per  degree  per  mm.  of  A 

0.1418  div. 

0.  0393  div. 

0.  0227  div. 

Ratio  of  efficiency  per  mm.  of  A 

6.25 

1.73 

1.00 

Ratio  of  efficiency  per  sq.  mm.  of  A/2 

7.52 

2.20 

1.00 

13 


The  relative  efficiency  of  unit  area  of  the  bolometer  is  diminished  by  the  use  of  an  excessive 
battery  current,  which  evolves  so  much  heat  that  it  can  not  be  dispersed  rapidly  enough  in  the 
rather  limited  chamber  of  the  bolometer  case  to  prevent  undue  increase  of  the  primitive  excess 
(<!— <0),  thereby  diminishing  the  increment  (<z— <i),  due  to  radiation.  A  comparison  of  the  relative 
efficiencies,  given  in  the  last  lines  of  Tables  3  and  4,  and  of  the  heat  developed  by  the  battery 
current,  shows  that  whereas,  with  equal  currents,  the  single-strip  bolometer  is  actually  about 
seven  and  one-half  times  as  efficient  as  the  23- strip  instrument,  the  heat  being  nearly  eight  times 
as  great  in  the  latter,  reduction  of  observations  made  with  unequal  currents  makes  the  computed 
efficiency  of  the  single-strip  instrument  for  equal  currents  only  about  three  times  that  of  the  other, 
when  the  heat  in  the  single  strip  is  over  seven  times  as  great  as  in  the  23-strip  bolometer. 

On  the  other  hand,  -the  probable  errors  of  single  observations  maintain  much  the  same 
relation  when  the  order  of  excessive  heating  by  the  current  is  reversed.  The  deflections  with 
uniform  current  are  by  no  means  inversely  proportional  to  the  exposed  areas,  as  the  last  line  of 
Table  4  shows,  the  deflection  per  square  millimeter  being  much  greater  for  the  smaller  instru- 
ments; but  this  can  not  be  due  entirely,  or  mainly,  to  diminished  values  of  t}—  #0  for  the  smaller, 
as  compared  with  the  larger  instruments,  for  otherwise  there  should  be  a  reversal  of  efficiency 
when  the  order  of  excessive  heating  is  reversed,  and  at  least  some  change  in  the  relation  between 
probable  errors. 

One  other  factor  remains  to  be  considered — the  form  of  the  bolometer.  It  is  evident  that 
a  large  part  of  the  heat  in  the  strips  is  removed  by  convection,  and  that  convection  is  much 
impeded  in  the  double-layer,  alternate-aperture,  gridiron -pattern,  or  multiple-strip  bolometer, 
while  in  a  single  strip  instrument,  or  one  of  few  and  narrow  strips,  the  adherent  sheaths  of  heated 
air  slip  from  the  metal  much  more  readily.  The  primitive  excess  of  temperature  is  much  less, 
therefore,  in  the  simpler  bolometer,  and  the  excess  imparted  by  radiation  is  greater.  It  is  difficult 
to  give  a  mathematical  expression  for  this  factor,  but  the  experiments  described  in  the  foregoing 
pages  indicate  its  importance.  The  removal  of  hot  air  by  convection  is  not  a  perfectly  continuous 
process,  but  an  alternation  of  instants  of  quiescence,  during  which  heat  accumulates,  and  the 
establishment  of  miniature  whirlwinds,  by  which  the  hot  air  is  swept  away.  The  irregularities 
thus  produced  account  for  the  larger  probable  errors  in  those  instruments  where  convection  is 
least  impeded.  If  the  battery  current  is  reduced  until  the  probable  error  for  one  observation  is 
the  same  in  every  case,  there  is  little  difference  between  the  deflections  from  single-strip  and 
multiple-strip  bolometers  of  the  same  metal. 

In  the  next  experiment  the  mean  temperature  of  excess  of  the  bolometer  strips  (T),  corre- 
sponding to  (tl  —  t0)  m  Professor  Eeid's  formula,  was  calculated,  by  Callendar's  formula*  for 
platinum  resistance,  from  the  measured  resistances,  when  different  currents  (C1)  were  used. 

TABLE  5. 


Current  C. 

Temperature 
excess  (T). 

C* 

09 

T 
T-z 

Ampere. 

C.  ° 

Ci  —  0.0011 

Tt—  0.0 

C.2  =  0.0119 

r»=  0.6 

1.000 

1.000 

C3  =  0.0279 

T3=  3.6 

5.497 

6.000 

C.(  =  0.0427 

T4  =  10.  4 

12.  875 

17.  333 

C-,  =  0.0505 

T,  =  15.  8 

18.008 

26.  333 

The  last  two  columns  show  that  the  mean  temperature-excess  increases  more  rapidly  than  the 
square  of  the  current,  indicating  that  the  confinement  of  parts  of  the  circuit  and  the  impeding  of 
convection  are  responsible  for  the  departure. 

Returning  now  to  the  experiments  described  on  page  7,  et  seq.,  the  following  temperature- 
excesses  are  indicated  for  the  bolometer,  by  the  measures  in  Table  5: 

(1)  Battery  current,  G\  —  0.026  amp.,  temperature-excess,  Tl  =  3°.0  C. 

(2)  "  "        Cz  —  0.032  amp.,  "  "       T2  =  5°.0  C. 

*  R  =  1  +  0.00346  T.  (See  La  Lumitre  Electrique,  January  8, 1887,  p.  78.)  Measurements  of  the  resistance  of  the 
same  bolometer  at  constant  temperatures,  in  summer  and  winter,  agreed  well  with  this  law. 


14 

The  heat  generated  by  the  current  in  the  second  case  is  to  that  in  the  first  as  (0.032)2  : 
(0.026)2  =  1.515. 

The  temperatures  maintained  are  in  the  ratio:  5.0:  3.0  =  1.67. 

The  ratio  for  the  central  part  of  the  strips  where  the  radiation  is  received,  will  be  smaller 
than  this,  as  has  been  pointed  out  before  (inequality  3) ;  but  this  will  not  affect  the  argument,  since 
the  diminution  of  the  temperature-ratio  is  accompanied  by  an  increase  of  the  factor  for  convection. 

A  comparison  of  the  loss  of  heat  from  thin  strips  and  from  the  spherical  bulb  of  a  small 
thermometer  is  instructive.  Experiment  has  shown  that  the  thermometer  at  corresponding 
temperature-excesses 

T!  =  3°.0,  cools  0°.71  per  minute. 
T2  =  5°.0,  cools  1°.24  per  minute. 

The  dimensions  and  water-equivalent  of  the  thermometer  bulb  were  such  that  these  repre- 
sent, respectively, 

0.001032  small  calories  per  sq.  cm.  per  sec. 
and  0.001802      "  "          «        "         "      " 

The  platinum  in  one  arm  of  the  bolometer  had  a  water-equivalent  of  about  0.00002  gram,  and 
the  heat  developed  in  it  by  the  current  was: 

(1) 


Q9     vx    1  A9 

x  0.026  x  10-'  )2  x  ~  1=  =  0.00129  calory  per  sec. 

4.2  x  10' 


(2) 


X  0.032  x  10-1)2  x 


v., 

j  * 


=  0.00195 


The  cooling  in  the  two  cases  must  have  been : 

(1) 

n  on 1 QK 

=  97°.5    "      " 


0.00129       .„ 

T>  =  64°.o  per  sec. 


0.00002 
0.00195 
0.00002 


which,  as  the  temperature-excesses  are  so  much  smaller,  shows  that  the  strips  lose  the  greater 
part  of  their  heat  in  a  small  fraction  of  a  second.  The  total  area  (both  sides)  of  the  platinum 
being  about  0.6  sq.  cm.,  the  losses  are 

(1)  0.00215  small  calory  per  sq.  cm.  per  sec. 

(2)  0.00325     "          "        "         "         «    '  " 

taking  place  partly  by  radiation  through  the  limited  aperture  of  the  ebonite  frame  holding  the 
strips,  and  partly  by  convection  from  a  surface  whose  ratio  to  the  volume  is  about  3,000  times 
as  great  as  that  of  the  thermometer  bulb.  In  the  thermometer  I  have  determined  the  loss  by 
convection  as  a  percentage  of  the  total  loss,  getting  the  values  in  the  following  table: 

TABLE  6. 


T. 

Convection. 

T. 

Convection. 

o 

Per  cent. 

C 

Per  cent. 

1 

6.5 

9               24.8 

2 

11.0 

10              25.  8 

3 

14.5 

11              26.  7 

4 

17.0 

12              27.  4 

5 

19.2 

13              28.  0 

6 

21.0 

14              28.  6 

7 

22.5 

15              29.  2 

8               23.7 

16              29.  8 

By  the  measurements  of  Dr.  J.  T.  Bottomley  *  on  the  emissivity  of  wires  in  vacuum  and  in 
air,  it  is  evident  that,  in  a  wire  0.2  mm.  thick  at  temperature-excesses  of  150°  and  200°  C.,  con- 


'  Phil.  Trans.  Royal  Soc.  London,  1887  (A),  p.  429. 


15 

vectiou  is  about  fifty  times  as  groat  as  radiation,  which  is  probably  clue  to  the  readiness  with 
which  successive  sheaths  of  heated  air  slip  off  from  such  a  surface.  Suppose  the  thickness  of  the 
air  sheath  to  be  ten  times  that  of  the  wire,  air  to  the  depth  of  2  mm.  being  heated  by  molecular 
interchange.  The  adhesion  between  the  two  must  be  very  slight,  but  increases  with  the  diameter 
of  the  wire. 

I  have  been  unable  to  determine  the  convective  ratio  for  a  bolometer,  but  it  is  probably 
safe  to  assume  that  it  is  intermediate  between  that  of  a  wire  of  diameter  the  same  as  the  width  of 
a  single  bolometer  strip  (about  0.2  mm.),  and  a  thermometer  bulb.  Simply  as  an  illustration,  we 
may  suppose  the  convection  ratio  is  seven  times  as  great  as  for  a  bulb.  For  small  excesses,  the 
radiation  may  be  taken  proportional  to  the  rise  of  temperature,  and  increasing  the  convection  ratios 
in  the  preceding  table  in  the  proportion  7:  1,  we  have: 


(1)  T!  =  3°.0 

(2)  T-2  =  5°.0 


Radiation  +  convection  =  1.00  +  (7  x  .145  x  1.00)  =  2.015. 
Radiation  +  convection  =  1.67  +  (7  x  .192  x  1.67)  =  3.914. 


Ratio  of  total  losses  =  =  1.942. 

2.01o 

In  (2)  the  temperature  being  67  per  cent,  greater  than  in  (1),  the  losses  are  10.3  per  cent. 
greater  than  a  simple  proportion  to  the  losses  at  the  lower  temperature,  and  the  rise  of  tempera- 
ture produced  by  a  constant  radiation  is  correspondingly  less  effective  in  changing  the  resistance 
of  the  bolometer,  which  may  be  expressed  in  terms  of  galvanometer  current  by  multiplying  the 
computed  relative  efficiency  of  the  two  arrangements  of  the  bridge  (p.  7)  by  1.163,  giving  the 
corrected  ratio 

_^il)  =  1.339  x  1.163  =  1.557, 

^5  (2) 

which  is  not  far  from  the  observed  ratio,  1.555,  now  finally  adopted.  For  equal  currents  this  ratio 
becomes  1.9  L,  and  by  this  factor  all  deflections  taken  with  the  insensitive  arrangement  of  the 
bridge  have  been  multiplied. 

The  value  assumed  for  the  convection  ratio,  according  to  this  test,  is  slightly  too  large;  but 
in  any  case  it  can  not  be  quite  correct,  since  no  allowance  has  been  made  for  thermal  conduction 
in  the  thin  strips.  I  am  not  able  at  present  to  give  an  estimate  of  this  factor,  but  the  following 
experiment  makes  its  existence  probable  in  metal  as  thin,  or  very  nearly  as  thin,  as  that  used 
for  bolometers. 

I  first  heated  the  front  surface  of  a  sheet  of  platinum,  4  /u  thick  and  blackened  on  both  sides, 
by  radiation  from  a  lamp,  and  measured  the  increment  of  radiation  from  the  rear  surface  of  the 
platinum  by  means  of  a  bolometer  which  was,  of  course,  completely  shielded  from  the  direct  rays 
of  the  lamp.  Xearly  two  minutes  were  consumed  in  reaching  a  maximum  deflection.  Fearing 
some  secondary  effect,  due  to  the  gradual  heating  of  the  perforated  screens  which  limited  the 
bundle  of  rays  falling  on  the  platinum,  the  experiment  was  modified  as  follows:  The  sheet  of 
blackened  platinum  covered  the  aperture  of  the  bolometer  case  and  was  in  turn  protected  by  a 
double  cardboard  screen  with  2-cm.  circular  apertures  centrally  situated.  A  sunbeam  of  5.7  cm. 
circular  section,  kept  fixed  by  a  heliostat,  fell  upon  a  concave  mirror  of  150  cm.  focus,  and  the 
solar  image  was  formed  upon  the  center  of  the  platinum  foil.  As  before,  the  radiation  from  the 
rear  surface  of  a  sheet  of  platinum,  receiving  heat  from  the  front  by  direct  radiation  on  a  very 
small  part  of  its  area,  was  to  be  measured.  The  sky  was  quite  clear  —  the  time  from  11  to  12  a.  m. 
All  exposures  were  made  by  withdrawing  a  distant  screen  placed  in  the  path  of  the  sunbeam. 
The  results  contained  in  the  following  table  show  that  much  the  larger  part  of  the  heat,  being  of 
course  that  of  the  small  area  embraced  in  the  solar  image,  is  obtained  within  the  first  ten 
seconds.  The  subsequent  progressively  diminishing  increments  can  not  be  attributed  to  any 
heating  of  the  bolometer  case,  since  the  insertion  of  a  neutral  screen  behind  the  platinum  made 
very  little  change  in  the  deflection. 


16 

TABLE  7. 

PLATINUM  HEATING  IN  SUNSHINE. 


0s 

10s 

20s 

30' 

40' 

50' 

60' 

70» 

80' 

90'              100' 

3i.'               120- 

0 
0 
0 

183 
193 
187.4 

193 
204 
196.8 

203 
215 
205.2 

208 
223 
212.6 

213 
228 
216 

215 
231 
220.6 

216.5 
233 

221.8 

217.  7       217.  5 
234.  7       236.  3 
223.  5       225.  4 

219.0 
239.1 
225.1 

227.7 

219.5       220 
238.  9       239.  1 
224.4       225.6 

Mean. 

187.8 

197.9 

207.7 

214.5 

219.0 

222.2 

223.  8       225.  3       226.  4 

i 

227.  6       228.  2 

PLATINUM  SHADED—  COOLING. 

220 
239.1 
225.6 

49 
53 
49.8 

40 
42 
40.7 

28 
29 
27.1 

19.6 
21 
18.5 

14.4 
15 
13.1 

11.4 
11.2 
10.3 

8.2 
8.3 

7.7 

6.0 
5.3 
5.3 

3.9 
3.9 
3.5 

2.4 
2.2 
1.9 

0.8           0 
1.1           0 
0.4  !        0 

Mean. 

50.6 

40.  9         28.  0 

19.7         14.2         11.0           8.  1  ;        5.5 

3.8 

2.2 

0.8  i        0 

Two  minutes  are  consumed  in  attaining  the  maximum  radiation,  and  tbe  same  in  cooling. 
The  whole  of  this  retardation  is  not  to  be  attributed  to  the  slowness  of  conduction  in  the  thin 
metal.  A  portion  of  the  effect  is  due  to  the  time  required  to  establish  a  heat  gradient  in  the  air 
near  the  heated  strip.  The  temperature  acquired  by  the  thin,  blackened  platinum  in  full  normal 
sunshine  is  such  as  could  be  developed  by  the  sun's  rays  in  less  than  one  tenth  of  a  second  if  all 
were  absorbed.  The  same  radiation  is  capable  of  heating  an  air  layer  around  the  platinum  4.5 
mm.  deep  to  the  same  temperature  as  the  platinum  in  the  same  time,  and  there  must  be  perpetual 
transfer  of  heat  from  the  metal  to  some  such  layer  of  air  in  a  bolometer  exposed  to  full  sunshine, 
since  more  heat  is  lost  by  convection  than  by  radiation.  How  much  of  the  heat  in  the  experiment 
just  described  has  been  transferred  from  the  focus  to  surrounding  parts  by  conduction,  and  how 
much  to  parts  above  the  focus  by  convection,  can  perhaps  be  determined  in  a  repetition  by 
mapping  the  distribution  of  heat  in  the  foil,  using  a  bolometer  case  of  very  small  angular  aperture. 

It  is  evident  from  the  foregoing  studies  that  the  thin  metal  strips  of  a  bolometer  had  best  be 
supported  by  stout  metal  arms  at  a  distance  from  all  insulating  or  obstructing  partitions.  Such 
an  instrument  has  not  been  used  in  the  present  measures,  but  it  is  hoped  that  by  keeping  the 
conditions  nearly  the  same,  the  results  may  still  be  capable  of  statement  in  terms  of  absolute 
measurement. 

The  actual  bolometer  used  exposes  a  surface  of  19.0  sq.  mm.,  divided  into  fifteen  strips,  the 
total  exposed  strip-length  being 

A  =  15  x  5.1  =  76.5  mm. 

The  methods  used  in  standardizing  the  instrument  will  be  described  under  the  head  of 
"  Screens." 

THE   GALVANOMETER. 

The  astatic  reflecting  galvanometer  has  a  resistance  of  20.5  ohms  at  20°  C.  Its  chief  pecul- 
iarity is  the  needle,  which  is  provided  with  hollow,  cylindrical  magnets  of  very  hard  steel,  arranged 
in  four  groups  of  five  each,  on  opposite  sides  of  a  straight,  supporting,  hollow  glass  fiber.  Each 
group  consists  of  one  magnet  9.5  mm.  long,  two  magnets,  each  8.5  mm.  long,  and  two  of  6.0  mm. 
length,  arranged  symmetrically  on  pieces  of  mica,  the  cylinders  being  fastened  by  shellac  and 
kept  from  contact  with  each  other  by  minute  bits  of  paper.  The  magnets  are  all  of  one  diameter, 
1.3  mm.,  and  the  weights  of  the  various  parts  of  the  needle  are  as  follows: 

nags. 
Twenty  hollow  cylindrical  magnets 219.  2 

Concave  mirror  of  platinized  glass 63.  0 

Glass  fiber  (139  mm.  long) 32.1 

Copper  suspension  ring 2.  0 

Mica,  paper,  and  shellac 17.  3 


17 

In  order  to  balance  the  mirror,  attached  to  the  west  face  of  the  upper  system,  and  make  the 
supporting  glass  fiber  hang  centrally  in  its  well,  a  platinum  vane,  pointing  east,  was  attached  at 
the  lower  end  of  the  glass  fiber,  bringing  up  the  total  weight  of  the  needle  to  a  little  over  350 
milligrams. 

The  rigidity  of  the  needle  is  sufficient  to  resist  the  very  slight  strain  experienced  .during 
an  ordinary  free  deflection,  but  accidental  maladjustment  has  sometimes  to  be  corrected,  and  the 
method  used  in  astaticizing  may  be  of  interest  to  those  who  work  with  similar  instruments. 

In  a  system  as  delicately  constructed  as  this  is,  a  slight  knock  or  pressure  is  liable  to  disturb 
the  parallelism  of  the  planes  of  the  upper  and  lower  systems.  Hence,  if  the  upper  and  stronger 


system,  indicated  by  the  full  line  (NS)  in  fig.  2,  has  its  plane  displaced,  so  that  its  north-seeking 
poles  lie  on  the  east  side  of  a  vertical  plane  through  the  lower  system  (N'S1),  there  is  a  resultant 
magnetism  at  right  angles  to  the  mean  plane  of  the  system,  and  with  its  north-seeking  poles  on 
the  east  side  of  that  plane.  This  resultant,  combined  with  the  original  residual  of  the  partially 
astatic  system,  turns  the  normal  to  the  mirror  (P)  to  the  south  of  the  west  point.  Some  care  is 
necessary,  therefore,  to  secure  an  approach  to  astaticism  and  at  the  same  time  to  keep  the  mean 
plane  of  the  system  in  the  magnetic  meridian.  The  following  mode  of  astaticizing  has  been  found 
advantageous,  and,  with  care,  can  be  applied  without  dismounting  the  delicately  suspended 
needle. 

The  upper  system  having  the  greater  capacity  for  retaining  magnetism,  whatever  diminution 
of  magnetism  is  necessary  has  been  made  on  this  system.  The  lower  system  is  first  magnetized  to 
saturation  by  a  large  magnet.  Next  the  magnetism  of  the  upper  system  is  brought  to  a  slight 
excess  by  making  judicious  passes  with  the  large  magnet  at  a  distance  of  1  cm.  or  less.  Finally, 
the  magnetism  of  the  upper  system  is  diminished  very  gradually  by  stroking  the  individual 
magnets  with  minute  bits  of  magnetized  needles  set  in  marked  wooden  handles,  the  free  north- 
seeking  or  south-seeking  poles  projecting  slightly. 

Suppose  that,  the  normal  to  the  mirror  pointing  west,  the  upper  system  is  stroked  on  its  east 
side  by  the  little  magnets. 

(1)  Strengthening  south-seeking  poles  inclines  normal  north. 

(2)  Strengthening  north-seeking  poles  inclines  normal  south. 

(3)  Weakening  south  seeking  poles  inclines  normal  south. 

(4)  Weakening  north-seeking  poles  inclines  normal  north. 

In  case  the  relative  position  of  the  planes  has  been  very  much  disturbed  by  these  gentle 
strokings,  if,  for  instance,  the  normal  to  the  mirror  turus  strongly  to  the  south  after  weakening  the 
south-seeking  poles  of  the  upper  system,  it  may  be  necessary  to  strengthen  the  south-seeking  poles 
of  the  lower  system  by  the  large  magnet:  or  if  the  reverse  disturbance  of  the  planes  has  occurred 
and  the  normal  inclines  strongly  to  the  north,  the  north-seeking  poles  of  the  lower  system  may 
have  to  be  strengthened.  The  reasons  for  the  above  rules  will  be  evident  from  the  figure.  Thus 
in  the  application  of  (3)  pressure  from  the  east  at  8  opens  the  angle  between  the  planes  of  the 
system,  as  in  fig.  2.  The  resultant  systems,  N'S  and  N8r,  are  developed,  which  tend  to  set  in  the 
plane  of  the  meridian.  At  the  same  time  the  directive  force  of  NS  has  been  weakened.  In  (4) 
pressure  being  applied  on  the  east  side  of  ^V,  the  opening  of  the  angle  between  the  planes  of  N8 
N'S'  is  the  opposite  of  that  in  fig.  2,  and  the  resultant  magnetic  systems,  SN',  S'N,  having  their 
south- seeking  poles  on  the  east  side  of  the  mean  plane,  tend  to  rotate  P  to  the  north,  the  directive 
12812— Bull.  G 2 


18 

force  of  N8  being  diminished  as  before.  In  (1)  the  pressure  tends  to  open  out  the  angle  as  in 
fig.  2  and  swing  P  to  the  south,  but  the  directive  force  of  NS  being  increased,  tends  in  the 
opposite  direction,  and  it  might  not  be  certain  which  would  prevail.  The  rule,  however,  is  the 
result  of  experience. 

A  single  hollow  cylindrical  magnet  10  mm.  long,  suspended  by  a  very  fine  quartz  fiber, 
made  a  half  vibration  in  0.286  sec.  (specific  inagetism  =  135  0.  G.  S.  units  per  gram  of  steel). 
The  average  of  a  system  of  ten  magnets,  as  prepared  for  the  galvanometer  was  0.386  sec. 
(square  =  0.149).  In  1892  the  astatic  condition  of  the  needle  was  such  as  to  give  a  half 
vibration  in  10  seconds,  which  in  1894  had  diminished  to  8  seconds,  no  retouching  having  been 
made  during  the  interval.  The  ratios 

0.149 :102  =  1 :671 

0.149:  82  =  1:429 

would  represent  the  relative  directive  powers  of  the  partially  astatic  system  at  these  dates,  were 
it  not  that  the  magnetic  moments  are  not  inversely  proportional  to  the  squares  of  the  times  of 
vibration  in  a  needle  as  heavily  damped  as  this.  The  weight  of  the  magnets  being  about  0.2 

gram,  and  specific  magnetism  800  Gaussian  units  (  :  '-  per  iiigr.  of  steel  ),  or  80  C.  G.  S. 

SGC« 

units  per  gram  of  steel,  the  magnetic  moment,  if  all  the  magnets  pointed  one  way,  would  be 

0.2  x  80  =  16  C.  G.  S. 

Astaticized,  if  the  law  of  inverse  squares  of  the  times  were  followed,  the  magnetic  moments 
would  be 

(1892)        16  -^  671  =  0.0238  C.  G.  S. 

(1894)         16  -i-  429  =  0.0373 
the  ratio  of  which  is 

0.0238  -j-  0.0373  =  0.638. 

But  the  galvanometer  constant,  determined  by  an  entirely  independent  method,  does  not  differ 
much  from  inverse  proportionality  to  the  times  of  vibration,  the  field  magnetization  being  the 
same  in  all  cases,  a  result  which  is  to  be  attributed  to  the  damping  as  already  noted. 

The  absolute  value  of  the  galvanometer  constant,  together  with  a  calibration  of  the 
galvanometer  scale,  has  been  made  in  the  following  way :  The  battery  current,  measured  by  an 
independent  standardized  galvanometer,  was  passed  through  the  delicate  galvanometer,  shunted 
by  84  cm.  of  heavy  copper  wire,  0.494  cm.  in  diameter,  reading  the  deflections  of  the  sensitive 
instrument  with  various  extra  resistances  interposed  in  the  circuit;  and  the  resistances  of  shunt 
and  battery  were  determined  separately. 

The  battery  resistance  was  measured  by  the  "half  deflection  method"  in  which  di  being  the 
deflection  through  extra  resistance  R^  d%  is  a  deflection,  half  as  great,  obtained  with  extra  resist- 
ance .R2.  The  battery  resistance  is  r  =  R2  —  (2  BI  +  G),  where  G  is  the  resistance  of  the  shunted 
galvanometer,  here  practically  zero.  Three  trials  gave : 

d1  =  500  div.,     RI  =  460  ohms,  d-2  =  250  div.,  Rz  =  204  ohms,  r  =  52  ohms. 

<71  =  400     «       jR1  =  584      "  ^  =  200     "  _R2  =  25S      "  r  =  68       " 

^  =  300     «       ^  =  794      "  d2  =  150     «  ^  =  369      "  r  =  56       « 
Average  battery  resistance  =  59  ohms. 

The  resistance  of  the  shunt  was  measured  by  short-circuiting  it  by  a  plug,  when  the  very 
low  resistance  of  the  heavy  brass  connections  of  the  resistance  box  became  the  sole  shunt, 
reducing  the  galvanometer  deflection  almost  to  zero.  The  current  from  a  single  cell  of  gravity 
battery,  reduced  by  1.100  ohms,  was  passed  directly  through  the  galvanometer  thus  shunted,  the 
galvanometer  connections  being  opened  and  closed  by  a  key.  The  valuation  of  the  deflections 
was  made  by  repeating  with  shunt  short-circuited,  and  either  of  the  smaller  (hundredth  and 
fiftieth  ohm)  coils  in  its  place,  using  the  formula  for  shunts: 

C}        8 

c~8+G 

where  Ci  is  the  current  through  the  galvanometer,  C  the  total  current,  8  the  resistance  of  the 


19 

shunt,  and  G  that  of  the  galvanometer.     In  the  present  case,  however,  since  8  is  very  small 

or  or 

relatively  to  6?,  the  ratio  ^ — -^  is  substantially  equal  to  -^,  which  maybe  used  instead. 

Putting  in  the  plug  also  short-circuits  the  thermopile  currents  from  junctions  of  unlike 
metals,  and  changes  of  temperature  cause  these  to  vary,  but  by  reversing  the  galvanometer 
connections,  their  effects  may  be  partly  eliminated.  With  a  high-resistance  galvanometer  this 
trouble  would  cease. 

Galvanometer  connections,  direct  or  reversed,  are  denoted  by  d  and  r  in  the  following  table. 
Shunt,  open  or  plugged  (that  is,  short-circuited),  is  signified  by  o  and  p.  The  comparison  deflec- 
tions, in  the  last  column  but  one,  correspond  to  a  hundredth-ohm  coil,  and  to  half  the  deflections 
given  by  two  different  fiftieth-ohm  coils. 

TABLE  8. 


Plugged. 

Open. 

Plugged. 

Shunt. 

Plugged. 

Open. 

Plugged. 

Shunt. 

0.01  ohm.        Res.  shunt. 

3. 

div. 
—  3.0 
—  2.7 
—  4.1 

ro 
div. 
—15.0 
—18.2 
—20.6 

rp 
div.                div. 
—  3.  0     —    17.  9 
—  7.0 
—  6.0     —(—4.3) 

dp 
div. 
+22.5 
+20.0 

+21.8 

do 
div. 
+33.1 
+35.5 
+37.6 

dp 
div. 
+20.4 
+21.2 
+18.8 

div. 
+       35.4 

—      20.8 

div. 
162.9 
153.2 
172.0 

ohm. 
13.6X0.01 

163 
=0.00083 

19.3x0.01 

—  3.3 

—17.  9         —5.3     —    13.  6 

+21.4 

+35.4 

+20.1 

+       13.6 

162.7 

dp 
+11.7 
+12.4 
+13.5 

do 
+36.9 
+33.0 
+33.8 

dp 
+15.2 
+18.0 
+18.7 

+    34.6 
—    W.9 

rp 
+  2.9 
+  1.2 
+  1.6 

ro 
—20.0 
—19.2 
-22.0 

rp 
—  5.2 
—  4.8 
—  3.7 

—       20.4 
-  (-1.4) 

133.4 
142.1 
159.5 

145 

=0.  00133 

+12.5 

+34.6 

+17.3 

+    19.6 

+  1.9 

—20.  4         —  4.  6 

—      19.0 

145.0 

Heavy  copper  shunt  reversed  and  solidly  clamped. 

dp 
+11.0 
+  9.9 
+11.5 

do 
+26.6 
+31.5 

+29.0 

dp 
+13.9 
+15.  2 
+15.5 

+     29.0 
-     12.9 

dp 
+13.9 
+15.  2 
+15.  5 

do 
+34.0 
+31.0 
+31.9 

dp 
+21.0 
+20.3 
+21.8 

+      32.3 
—      18.0 

122.1 
118.6 
147.8 
147.8 
162.8 
163.8 

15.2x0.01 

144 
=0.  00109 

16.3x0.01 

+10.8 

+29.0 

+14.9     +     16.1         +14.9 

+32.3 

+21.0 

+       14.3 

rp 
—  3.2 

—  2.0 
—  2.5 

ro 
—20.0 
—23.2 
—21.2 

'?  n 
—  5.0 

—  7.5 
—  6.2 

—    21.  5         —12.  0 
—16.0 
—(—4.4)        —13.6 

ro                     rp 
—31.  2         —20.  9 
—33.  0         —17.  2 
—31.  4,        —19.  1 

—      31.9 
-(-16.5) 

144 
=0.  00113 

—  2.6 

—21.5 

—  6.2 

•    17.1         —13.9         —31.9         —19.1 

—      15.4 

143.8 

Mean  resistance  of  hea1 

fy  shunt  '.  ...  

—0.00109 

In  the  galvanometer  tests,  induction  currents  gave  a  stronger  backward  swing  than  happens 
in  the  bolometric  work  where  there  is  a  continuous  current  only  slightly  varied  by  the  resistance 
changes  due  to  radiation.  Consequently  deflections  have  been  computed  by  a  formula: 


«1 


2 

where  e\  is  the  reading  before  connecting,  d  the  extreme  of  the  swing  given  by  the  current,  and  6', 
is  obtained  from  three  successive  swings  of  the  needle,  after  the  current  is  broken,  by  the  formula: 


A  single  series  follows  in  full  (extra  resistance,  270  ohms). 


20 
TABLE  9. 


., 

d 

P*j 

* 

„ 

<-,+*, 

s 

2 

+2 

+405 

—111             +35 

_3 

+4.9 

+3.  5     +401.  5 

0 

•403 

—117             +30 

-5               +1.7 

+0.  9         402.  1 

+1               397 

—116 

+30 

—  5 

+1  8 

+1.4 

395.6 

0              389 

—114 

+29 

—  fr 

+0.9 

+0.5 

388.5 

+1              389 

—115 

+26 

—  7 

-0.7 

+0.2 

388.8 

0 

388 

—113 

+30 

—6               +1.  2 

+0.6 

387.4 

+1 

395 

—115 

+31 

—3               +3.  4 

+2.2 

392.8 

—1 

396 

—118 

+27 

—9              —  1.  8 

—1.4 

397.4 

i 

396 

—113 

+33 

—2               +4.  8 

+1.9 

394.1 

+2 

396 

—111 

+30 

—4               +2.  6 

+2.3 

393.  7 

+0.5 

+395.  4       —114.  3 

+30.0 

—5.0           +1.9 

+1.2 

+394.  2 

The  ratio  of  the  current  in  the  galvanometer  to  that  in  the  shunt  is  taken  as  1 : 18,800. 
The  mean  results  of  five  series  are  given. 

TABLE  10. 


Series. 

Extra  resistance 
plus  battery. 

Current  in                  Deflection, 
shunt.                               5 

Current  in 
galvanometer. 

Galvanometer 
constant.   ldiv.= 

1 
2 
3 
4 
5 

Ohms. 
1,159 
609 
429 
329 
269 

Ampere. 

0.  00735 
0.01399 
0.  01986 
0.  02590 
0.  03167 

Divisions. 
114.7 
211.6 
298.5 
394.2 
484.2 

Ampere. 
3.  91X10-7 
7.44 
10.56 
13.78 
16.85 

Ampere. 
3.40xlO-y 
3.51 
3.53 
3.50 
3.48 

Mean  galvanometer  constant,  1  div.  =  3.  48x10  ~9  ampere. 

It  will  be  seen  that  the  galvanometer  constant  is  the  same  in  all  parts  of  the  scale,  as  nearly 
as  can  be  determined  by  this  method.  There  have  been  some  indications  that  the  instrument  is  a 
very  little  more  sensitive  for  small  deflections,  less  than  20  div.;  but  as  the  amount  is  hardly 
appreciable,  and  seem's  to  vary  with  the  slightest  change  in  the  hanging  of  the  needle,  no 
correction  has  been  applied. 

Since  the  cylindrical  magnets  do  not  lie  in  the  central  plane  of  the  coils,  the  induction  damp- 
ing is  larger  than  usual,  and  departure  from  a  logarithmic  decrement  was  to  be  anticipated  in  the 
vibrations.  The  means  of  the  five  series,  similar  to  that  given  in  full  in  Table  9,  are: 

TABLE  11. 


«I 

d 

n, 

n2                     n3 

«2 

•t+4 

& 

2 

+0.3 

+115.  1 

—  31.2 

+  8.6           —1.7 

+0.5 

+0.4 

+114.7 

+0.2 

+211.7 

—  60.3 

+15.  5           —4.  11      "  +0.  0 

+0.1 

+211.  6 

—0.2 

+298.  9 

—  86.3 

+23.  3           —4.  9 

+1.0 

+0.4 

+298.  5 

+0.5 

+395.  4 

-114.  3 

+30.  0           —5.  0 

+1.9 

+1.2 

+394.  2 

+0.6 

+484.  0 

—141.  6 

+34.  6           —9.  3 

—0.9 

—0.2 

+484.  2 

The  next  table  contains  the  amplitudes  (cii  0%  a3)  of  successive  vibrations  and  the  logarithms 
of  their  ratios. 

TABLE  12. 


a, 

at 

«3 

< 

1        a, 

2^ 

146.3 
272.0 
385.2 
509.7 
625.6 

39.8 
75.  8 
109.6 
144.3 
176.2 

10.3 
19.6 
28.2 
35.0 
43.9 

0.  5651 
0.  5550 
0.  5560 
0.  5460 
0.  5503 

0.  5766 
0.  5713 
0.  5678 
0.  5816 
0.  5769 

Mean  logarithmic  decrements. 

0.  5545 

0.574!) 

The  air  damping  appears  to  be  tolerably  uniform,  since  there  is  no  marked  relation  between 
the  logarithmic  decrements  and  the  amplitudes;  but  the  influence  of  induction  currents  is  seen  in 
the  change  Of  the  decrement  in  successive  periods. 

The  needle  is  suspended  by  a  single  fiber  of  silk,  33  cm.  long  from  the  suspending  piece  to  the 
copper  ring.  The  entire  fiber  is  about  40  cm.  long,  is  tied  to  the  copper  ring  of  the  needle  by  a 
loose  square  knot,  and,  at  its  other  end,  carries  a  weight  equal  to  that  of  the  needle.  At  the  outset 
the  galvanometer  is  inverted,  and  the  counterpoise  hanging  freely,  the  silk  fiber  is  allowed  to 
stretch  and  untwist  until  it  comes  into  a  normal  state;  then  the  galvanometer  is  set  up  in  its 
usual  position,  the  fiber  passing  over  the  edge  of  the  suspending  piece,  but  not  being  fastened 
to  it.  The  suspending  piece  is  finally  adjusted  until  the  needle  hangs  centrally.  As  thus  pre- 
pared the  silk  fiber  has  very  little  tendency  to  twist,  the  image  from  the  free  but  undisturbed 
needle  seldom  wandering  during  the  day  more  than  the  few  divisions  to  be  expected  from  the 
diurnal  variation  of  the  magnetic  declination. 

The  bolometric  equilibrium  can  not  be  maintained  perfectly  in  a  room  of  changing  temperature, 
and  some  means  of  bringing  the  null  point  to  any  part  of  the  scale  at  pleasure  is  desirable. 
Variation  of  the  field  by  weak  magnets,  although  objectionable,  has  been  used  to  some  extent. 
The  change  of  field  necessary  in  order  to  push  the  null  point  from  one  end  of  the  scale  to  the  other 
was  determined  by  measuring  the  deflection  from  a  constant  impulse. 

TABLE  13. 


Startiiig    :  Mean    of   10  deflec- 
point.                       tions. 

Percentage 
of  deflection 
at  100. 

Division!. 

Per  cent. 

0 

+  87.  61+0.  34 

101.9 

100 

+85.  03+0.  38 

100.0 

200 

+84.  99+0.  39 

98.1 

300 

+81.27+0.51 

96.1 

400  i 

+80.  83+0.  72 

94.3 

In  order  that  the  deflections  may  be  Comparable  within  2  per  cent.,  the  null  point  should  not 
be  changed  by  more  than  100  divisions  during  the  observations.  To  avoid  the  necessity  of  more 
than  a  slight  change  of  field  the  electric  current  has  been  allowed  to  flow  through  the  bolometer 
for  at  least  twenty-four  hours  before  commencing  observations,  and  the  room  has  been  kept  at  a 
nearly  constant  temperature. 

The  cover  glass  of  the  galvanometer  case  has  optically  plane  parallel  surfaces,  and  the  carefully 
figured  mirror  gives  a  sharp  image,  permitting  readings  by  estimation  to  a  tenth  of  a  division. 

In  some  of  the  experiments  I  have  made  the  exposure  to  radiation  by  pulling  cords,  at  the 
same  time  reading  the  galvanometer ;  in  others,  it  has  been  necessary  to  have  an  assistant  shift 
some  part  of  the  apparatus  at  the  word  of  command. 


SCREENS. 

The  bolometer  chamber  has  been  used  with  two  different  openings :  First,  a  wide  aperture, 
limited  by  a  series  of  graduated  circular  card-board  diaphragms,  the  outermost  1.19  inches 
(3.02  cm.)  in  diarieter,  3.92  inches  (9.96  cm.)  from  the  bolometer,  giving  an  angular  aperture  of 
17°  16'.  Second,  a  smaller  aperture,  the  case  being  further  protected  by  triple  tin-plate  screens, 
with  circular  openings:  the  outermost  1.15  inches  (2.92  cm.)  in  diameter,  12.3  inches  (31.24  cm.)  in 
front  of  the  bolometer  (angle  5°  21'):  the  middle  and  limiting  aperture  1.02  inches  (2.59  cm.)  in 
diameter,  11.3  inches  (28.70  cm.)  from  the  bolometer,  giving  an  angular  aperture  of  5°  10'. 

The  ratio  of  the  squares  of  the  angular  apertures  is  11.17  :  1,  but  the  observed  efficiencies 
have  the  ratio  8.96  :  1,  which  is  adopted.  I  can  only  conjecture  that  the  difference  is  due  to 
the  reflection  of  the  bolometer's  radiation  by  the  polished  tin  plate,  and  the  retention  of  a  larger 
proportion  of  the  heat  received  from  radiation  when  the  aperture  is  partly  closed  by  the  metal 
screen;  but  no  experiments  have  been  tried  to  test  the  hypothesis. 


22 

In  order  to  transform  the  measures  made  in  arbitrary  units  of  a  scale  into  absolute  units  of 
radiant  energy,  and  at  the  same  time  to  furnish  a  check  on  the  constancy  of  the  measuring  instru- 
ments, the  bolometer  has  been  exposed  from  time  to  time  to  the  radiation  from  blackened  copper 
screens  containing  water  at  different  temperatures. 

The  unit  of  radiant  energy  employed  is  that  which  I  have  elsewhere  called  the  radim,* 
"representing  a  unit  quantity  of  heat,  namely,  one  gram- water-degree- centigrade  heat-unit,  lost 
as  radiation  per  square  centimeter  of  surface  per  second  of  time,  by  a  heated  body,  or  transmitted 
by  the  ether  as  an  equivalent  amount  of  radiant  energy  through  a  normal  section  of  1  sq.  cm.  in 
one  second  of  time." 

The  standard  of  radiation  adopted  is  that  of  blackened  copper  at  100°  C.  to  a  surface  of  the 
same  material  at  0°  C.,  filling  the  hemisphere,  which,  according  to  the  measures  of  Dr.  J.  T. 
Bottoinley  may  be  taken  as  0.0126  radiin.  Measured  radiations  between  any  other  temperature 
limits  have  been  reduced  to  the  standard  by  multiplying  by  a  factor  obtained  by  dividing  the 
difference  of  radiations  at  the  given  limits,  as  read  from  the  standard  curve  (derived  from  Table  B, 
p.  270,  Astropliysical  Journal,  Vol.  8),  by  0.0126.  The  deflections  are  further  reduced  to  a  standard 
battery  current  of  0.033  ampere,  corresponding  to  100  div.  of  the  battery  galvanometer. 

The  radiating  surface,  seen  through  the  full  aperture  of  17°  16',  occupied 

(50  x  tan  8°  38')2  X  n  =  181.06  sq.  cm., 

the  center  of  the  radiating  surface  being  placed  50  cm.  from  the  bolometer,  and  its  plane  normal 
to  the  line  of  sight.  The  mean  angle  with  the  line  of  sight  of  a  circle  in  the  radiating  surface  at 
mean  distance  is 

a  —  tan  -1  ^— -?-  =  6°  7'  .7, 
2  x  50 

where  the  radius  of  the  bounding  circle  is 

r  =  50  x  tan  8°  38'; 
and  the  mean  distance  of  the  surface  is 

d  =  ^2   =  50.319  cm. 
2  sin  or 

The  bolometer  of  0.19  sq.  cm.  receives  of  the  total  radiation,  assuming  equable  emission  at  all 
inclinations,  the  fraction 

Jill?  =  0.000  Oil  957 


and  the  standard  radiation  received  by  the  bolometer  with  full  aperture  is 

El  =  0.000011957  x  181.06  x  0.0126. 
=  0.000  027  278  radim. 

The  smaller  aperture  has  been  used  with  radiators  but  little  removed.    The  radiation  through 
*  The  Probable  Kange  of  Temperature  on  the  Moon,  Astrophysical  Journal,  vol.  8,  p.  271,  December,  1898. 


23 

this  aperture,  of  1.295  cm.  radius,  is  virtually  that  of  a  surface  of  like  area,  5.2685  sq.  cm.,  and  the 
standard  radiation  received  by  the  bolometer  is 


=  0.000  002  437  radim.  * 

The  efficiency  of  the  radiation  coming  through  this  smaller  aperture,  however,  has  been  shown 
to  be  25  per  cent,  greater  than  that  of  an  equal  amount  of  radiant  energy  passing  through  the 
large  aperture  (p.  21). 

I  proceed  to  give  screen  comparisons  and  the  valuation  of  standard  deflections. 

March  12,  1892. 

FIRST  SERIES. 

Battery  galvanometer  100  div. 

Hot  screen  69°.8  C.,  computed  radiation  0.0154  radim. 
Cold     "        9°.5  C.,         "  "         0.0083      " 

Radiation  reduced  from  standard  : 

E=E2x~=  0.000  001  373  radim. 
12o 

d  =  35.43  div.  (mean  of  10.  small  aperture)  ;  1  div.  =  0.000  000  0388  radim. 
lar 
563.4  div. 


126 

Standard  deflection,  on  standard  radiation,  and  with  full  aperture  =  35.43  x  8.96  x      -= 


SECOND  SERIES. 

Battery  galvanometer  100  div. 

Hot  screen  69°.4  C.,  computed  radiation  0.0153  radim. 

Cold     "       110.80.,          "  "          0.0085      " 

68 
E  =  E2  x  -p>g  =  0.000  001  315  radim. 

S  =  30.94  div.  (mean  of  10,  small  aperture);  1  div.  =  0.000  000  0425  radim. 

126 
Standard  deflection  (full  aperture)  =  30.94  x  8.96  x  gg-  =  513.7  div. 

*The  quantities  E{  and  E2  are  introduced  purely  as  reduction  factors,  and  do  not  represent  exactly  the  quantities 
of  normal  radiation  received  by  the  actual  bolometer,  although  the  latter  may  easily  be  derived  from  them. 

The  total  radiation  from  each  unit  of  radiating  surface  to  a  hemisphere  is  to  the  fraction  of  radiation  emitted 
per  sq.  cm.  at  angle  (ii)  with  the  normal,  and  received  on  an  element  of  the  hemisphere  (Ss),  in  the  p  .oportion 

2  it  r  x  ^  ^  cos  i  sin  i  di  :  cos  ii  ds. 

In  the  present  case,  cos  ii  may  be  taken  as  unity,  Ss  (the  area  of  the  bolometer)  is  0.19  sq.  cm.,  5i  =  |  degree,  and 
r  —  28.7  cm. 

The  numerical  value  of 

2ier  x  ^^  cosisin  i  5i=  it  r  ^i  7rsin2i  x  — 
0  0  ooO 

is  2587.7,  and  the  bolometer  receives  0.19  -H  2587.7  =  -   --  of  the  entire  radiation. 

13619 

For  any  other  radiator  than  lampblack,  the  relative  radiation,  p  X  0  (i),  must  be  considered.  The  value  of  p 
has  been  determined  for  air  in  the  present  research  for  nearly  normal  emission,  but  0  (i)  remains  unknown. 


24 

July  28,  1892. 

Battery  galvanometer  97  div. 

Hot  screen  76°.0  C.,  computed  radiation  0.0162  radim. 

Cold     «        33°.8  O.,          "  "         0.0107  radim. 

55 
E  =  E,  x  jog  =  0.000  001  073  radim. 

-  !?  =  25.30  div.  (mean  of  10,  small  aperture) ;  1  div.  =  0.000  000  0424  radim. 


126 
Standard  deflection  (full  aperture)  =  25.30  x  8.96  x  -~-  =  519.3  div. 

March  10,  1893. 

Battery  galvanometer  98  div. 

Hot  screen  99°.0  C.,  computed  radiation  0.0200  radim. 

Cold     "         0°.8  C.,          "  "          0.0078      " 

E  -  E,  x  1  l2 '  =  0.000  026  412  radim. 
MI  x  126 

6  =  515.9  x  -Qg  =  526.4  div.  (mean  of  10,  full  aperture);  1  div.  =  0.000  000  0502  radim. 

126 
Standard  deflection  (full  aperture)  =  526.4  x  ^  =  543.7  div. 

March  3,  1894. 

Battery  galvanometer  101  div. 

Hot  screen  98°.7  C.,  computed  radiation  0.0200  radim. 

Cold    "         00.7  C.,         u  "          0.0078      « 

122 
E  =  Ev  x  ;£*  =  0.000  026  412  radim. 


6  =  ^jffi^  ~  =  482.6  div.  (mean  of  10,  full  aperture);  1  div.  =  0.000  000  0547  radim. 

126 
Standard  deflection  (full  aperture)  =  482.6  x  p^  =  498.4  div. 

March  30,  1894. 

Battery  galvanometer  95  div. 

Hot  screen  99°.l  C.,  computed  radiation  0.0200  radim. 

Cold     "       290.4  C.,         "  "         0.0103      « 

97 
E  =  El  x  126  =  0-000  °21  00°  radim- 

d  =  364.2  X  (jrj-  =  383.4  (mean  of  10,  full  aperture)  ;  1  div.  =  0.000  000  0548  radim. 

126 
Standard  deflection  (full  aperture)  =  383.4  x  97  =  498.0  div. 

July  30,  1895. 
Battery  galvanometer  95  div. 

FIRST  SERIES. 

Hot  screen  98°.3  C.,  computed  radiation  0.0198  radim. 
Cold     "       23°.7  C.,          "  "         0.0097      " 

E  —Ev  X         =  0.000  021  866  radim. 


6  =  456.1  x  93  =  480.1  (mean  of  10,  full  aperture)  ;  1  div.  =  0.000  000  0456  radim. 

1°6 
Standard  deflection  (full  aperture)  =  480.1  x      T  =  598.9  div. 


25 

SECOND  SERIES. 

Hot  screen  91°  0.,  computed  radiation  0.0187  radim. 
Cold     "       240  c.,          "  "         0.0097      " 

90 
E  =%!  X  jg6  =  0.000  019  484  radim. 

8  =  401.7  x  gl-  =  422.8  (mean  of  5,  full  aperture);  1  div.  =  0.000  000  0461  radim. 

126 
Standard  deflection  (full  aperture)  =  422.8  x  on  =  591.9  div. 

THIRD  SERIES. 

Hot  screen  85°  C.,  computed  radiation  0.0177  radim. 
Cold    "       24°  C.,         "  "         0.0097      " 

80 
E  =  El  x  pg  =  0.000  017  319  radim. 

d  =  354.8  x  g--  =  373.5  (mean  of  5,  full  aperture);  1  div.  =  0.000  000  0464  radim. 

126 
Standard  deflection  (full  aperture)  =  373.5  x  ^Q-  =  588.3  div. 

FOURTH  SERIES. 

Hot  screen  77°  C.,  computed  radiation  0.0164  radim. 
Cold     "       24°  C.,          "  «         0.0097      »< 


E  =  El  x  126  =  0<00°  °14  505  radilu- 

6  =  300.6  x  -gg-  =  316.4  (mean  of  5,  full  aperture)  ;  1  div.  =  0.000  000  0458  radim. 

126 
Standard  deflection  (full  aperture)  =  316.4  x  -gy-  =  595.0  div. 

The  last  four  series  were  made  to  test  the  validity  of  the  mode  of  reduction  for  E,  which  is 
sufficiently  accurate  for  its  purpose.  The  two  series  of  March  12,  and  that  of  July  28,  1892.  being 
founded  on  rather  small  deflections  taken  with  the  small  aperture,  are  less  reliable  than  the  others. 
They  give  a  mean  value  of  1  div.  =  0.000  000  0412  radim,  corresponding  to  0.000  000  0412  x  f  = 
0.000  000  0515  radim  for  the  full  aperture.  The  observation  of  March  10,  1893,  with  full  aperture, 
gave  1  div.  =  0.000  000  0502  radim,  and  the  galvanometer  constant  may  be  assumed  uniform  for 
the  first  year  (1892-93),  when  its  value  in  amperes  was  measured.  On  March  3,  and  March  30, 
1894,  larger  radiation  was  required  to  give  a  deflection  of  one  division,  namely,  1  div.  = 
0.000  000  0548  radim,  or  74-  per  cent,  greater  than  in  1892-93,  the  vibration  of  the  needle  having 
meanwhile  become  20  per  cent,  more  rapid,  or  the  squares  of  the  times  36  per  cent,  smaller;  and 
finally,  in  July,  1895,  the  time  of  vibration  being  the  same  as  in  1894,  1  div.  =  0.000  000  0460  radim, 
or  7£  per  cent,  less  than  in  1892-93.  The  last  change  is  perhaps  attributable  to  simultaneous 
changes  in  the  magnetism,  of  the  needle  and  in  the  magnetic  field,  but  as  the  field  was  not 
measured  independently,  no  correction  is  available. 

The  variation  of  the  radiator's  surface  is  a  possible  source  of  error  in  these  standardizings. 
To  guard  against  it,  a  uniform  procedure  has  been  followed.  The  screens  are  of  copper,  painted 
dead  black,  with  a  very  thin  coat.  Before  using,  this  surface  is  lightly  smoked  with  a  fresh  coat 
of  soot,  uniformly  distributed.  From  experience  with  such  a  surface,  it  does  not  seem  probable 
that  variations  of  more  than  2  or  3  per  cent,  are  to  be  anticipated;  but  it  is  not  asserted  that  this 
standard  fulfilled  the  ideal  of  an  absolutely  black  body.  After  the  measures  of  July  30,  1895,  an 
effort  was  made  to  carry  the  radiant  emissivity  of  the  hot  screen  somewhat  nearer  its  maximum 
value,  by  repeated  smokings,  while  the  screen  was  temporarily  filled  with  cold  water,  until  a  coat 
of  soot  i  mm.  thick  had  been  deposited.  The  mean  standard  deflection  of  593.5  was  thereby  raised 
to  620.7,  or  by  4.6  per  cent. 


26 

If  the  variations  are  attributed  to  errors,  and  all  observations  have  equal  weight,  1  div.  = 
0.000  000  0490  i  0.000  000  0010  radim,  but  in  the  author's  opinion,  it  is  best  to  accept  the 
variation  as  a  fact  and  to  take  the  valuations  as  given  at  the  stated  epochs,  whence,  for  full 
aperture,  we  have  the  following  radiant  values : 

(1892-93)     1  div.  =  0.000  000  0509  radim. 

(1894)  0.000  000  0548     " 

(1895)  0.000  000  0460     « 

For  the  small  aperture,  the  corresponding  values  are  four-fifths  of  these — 

(1892-93)     1  div.  =  0.000  000  0412  radim. 

(1894)  0.000  000  0438     " 

(1895)  0.000  000  0368     " 

PSYCHBOMETER   FACTOK. 

The  water- vapor  in  the  air  experimented  upon  has  been  measured  by  a  stationary  psychrom- 
eter,  checked  occasionally  by  a  dew-point  apparatus.  The  usually  adopted  formula  for  a 
ventilated  or  a  sling  psychrometer  is : 

/!  =/2  _  0.000  67  (t  -  t')  H, 

where  f\  =  the  pressure  of  water- vapor  at  the  dew-point,  /2  =  the  vapor  pressure  at  the 
temperature  of  the  wet  bulb,  and  H  =  the  barometer  reading,  may  be  in  either  millimeters  or 
inches  of  mercury;  but  t  and  t',  the  dry  and  the  wet-bulb  readings,  are  in  centigrade  degrees. 

The  statement  is  made  in  books  on  the  subject  that  the  numerical  factor  by  which  the 
difference  (t  —  t')  is  to  be  multiplied,  may  need  to  be  doubled  in  a  closed  room;  but  since  every 
psychrometer  must  vary  according  to  the  kind  of  muslin  with  which  the  wet  bulb  is  covered,  and 
according  to  the  disposition  of  objects  around  it,  the  factor  should  be  determined  by  experiment. 

Two  windows  on  opposite  sides  of  the  room  were  left  open,  producing  a  gentle  circulation 
of  the  air.  Dew  was  formed  on  a  polished  tin-plate  vessel  in  which  water  was  cooled  by  ice,  or 
heated  at  pleasure.  The  cold  water  half  filled  the  vessel,  and  the  contrast  between  upper  and 
lower  halves  was  noted. 

(1) 

0  C.  °  C. 


Dew  formed  at          +  6.8  1  M  g  - 

Dew  evaporated  at  +  9.4  j  1V 

(2) 


C.  °  C. 


Dew  formed  at         +  7.8  1  M  g  , 

Dew  evaporated  at  +  8.9  |  fl 


Observed  dew-point  =  +  8°.3  C.=+46°.9  F. 
Corresponding  psychrometer  readings  : 

c  F.      °  c.  °  F.       °  C. 

Dry  bulb  77.1  ^  25.0  i  Difference  13  9  _  7  7 
Wet  bulb  63.2  =  17.3  (  L 

(2) 

0  F.        °  C.  °  F.         °  C. 

Dry  bulb  77.6  =  25.3  )  Difff.rpn(  e  13  o  _  7  7 
Wet  bulb  63.7=  17.6  \L 

The  windows  were  now  closed. 

(In  ten  minutes.) 

(3) 


27 

(In  thirty  minutes.) 


(In  sixty  minutes.) 

(5) 

c  F.         °C.  CF.        °C. 

80.1  =  26.7 
68.1  =  20.0 

Open  icindows. 

By  Hazen's  Tables  (Fahrenheit,  p.  64)  for  the  temperature  77°  F.  and  dew-point  47°,  the 
depression  of  the  wet  bulb  (ventilated)  is  17°.25  F.  The  observed  depression  was  13°.9  F.,  whence 
(t—f)  must  be  multiplied  by 

factor  =  ™*  =  1.24 

For  the  temperature  77°.5  F.  (same  dew-point),  the  depression  by  the  table  is  17°.50  F.,  and 
the  observed  depression  13°.9  F. 


Windows  closed. 

For  the  temperature  79°  F.  (same  dew-point  as  before),  by  table,  depression  =  18°.o  F., 
observed,  12°.4, 

factor  =  iJ?  =  i-49 
1J.4 

For  the  temperature  80°  F.  (same  dew-point),  by  table,  depression  =  19°.0  F.,  observed,  11°.4, 

factor  =  i9^  =  1.6" 
11.4 

For  the  temperature  80°  F.  (same  dew-point),  the  final  observation  gave  depression  12°.0, 

factor  =  ^!?  =  1.58 

The  first  condition  (two  windows  open)  is  seldom  realized  in  bolometric  work,  and  never  unless 
the  outside  air  is  nearly  calm,  which  was  not  the  case  during  the  above  experiments.  In  winter 
the  windows  are  usually  closed  during  bolometric  observations,  this  being  necessary  to  prevent 
air  currents  and  sudden  variations  of  temperature  around  the  bolometer.  The  room  in  which 
the  experiments  were  made  has  a  floor  space  of  CO  sq.  m.,  and  is  connected  with  other  rooms,  all 
heated  by  a  hot-air  furnace,  and  well  ventilated.  In  warm  summer  weather  a  single  window  is 
commonly  open.  These  tilings  being  so,  since  the  mean  of  the  above  determinations  gives  1.45  for 
the  multiplier,  1.5  is  adopted  as  the  working  factor  by  which  (t  —  t1}  has  been  multiplied  in  finding 
the  dew-point  by  the  unventilated  psychrometer,  and  by  Hazen's  Tables.  With  this  explanation, 
further  details  will  be  omitted,  and  only  the  results  of  psychrometric  measures  will  be  stated. 

Three  successive  pieces  of  apparatus  have  been  used  for  measures  of  atmospheric  radiation : 

(a)  A  pair  of  open  radiant  cylinders. 

(6)  Hot  air  ascending  from  a  furnace  flue. 

(c)  A  closed  radiant  cylinder  with  movable  disk. 


28 

The  horizontal  air  column  in  line  with  the  bolometer  is  to  be  considered  as  composed  of  two 
parts.  The  portion  between  the  bolometer  and  the  front  of  the  radiating  apparatus  is  of  nearly 
the  same  temperature  as  the  bolometer,  and  acts  chiefly  by  absorbing.  The  portion  of  air  within 
the  apparatus  both  radiates  and  absorbs,  but  the  differential  effect  is  radiative,  and  for  the  sake 
of  distinction  the  first  part  may  be  called  the  absorbent,  the  second  the  radiant  layer. 

Psychrometer  readings,  as  usually  reduced,  are  stated  in  pressures  of  water- vapor  on  the 
standard  of  the  mercury  gage  (millimeters  of  mercury),  or  as  a  weight  of  wa'ter  per  unit  volume 
of  air  (grams  per  cubic  meter) ;  but  in  considering  the  absorbent  or  radiant  effects  it  is  more 
convenient  to  express  the  amount  of  water-vapor  as  a  depth  of  equivalent  liquid  water  penetrated 
by  the  line  of  sight  within  the  limits  of  the  radiative  or  absorbent  column.  For  example,  a 
column  of  air  100  meters  long  and  1  square  decimeter  in  section  occupies  1  cubic  meter,  and  if  its 
water- vapor  be  all  condensed  upon  a  normal  section,  a  liquid  layer  1  millimeter  thick  will  be 
produced  for  every  10  grams  of  vapor  contained  in  the  air  column.  If  the  volume  of  air  has  the 
form  of  a  cube  1  meter  on  an  edge,  the  layer  of  condensed  water  being  distributed  over  a  normal 
section  of  1  square  meter,  will  have  a  depth  of  0.01  mm.  for  every  10  grams  per  cubic  meter,  the 
depth  of  water  being  directly  proportional  to  the  length  of  the  air  column  multiplied  by  the 
absolute  humidity.  This  mode  of  expression  relates  solely  to  the  quantity  of  water  present. 
Nothing  is  predicated  as  to  the  quality  of  its  absorption  or  radiation,  which  may  vary  widely 
according  to  the  physical  state  in  which  this  definite  quantity  of  water  exists. 

The  chief  atmospheric  constituent  affecting  radiation  being  water-vapor,  it  is  necessary  to 
consider  the  air  depths  (d),  and  the  equivalent  layers  of  liquid  water  (w)  in  d,  for  each  gram  of 
water-vapor  per  cubic  meter  of  air,  involving  the  following  constants  in  the  successive  pieces 
of  apparatus. 

TABLE  14. 


Absorbent  layer. 


Radiant  layer. 


Apparatus  a 
Apparatus  bt 

Apparatus  bi 
Apparatus  c 


tv  =• 


d  ==  13.  2    inches  =  33.  5  cm. 

w  =  0.  000  0335  cm. 

rf=  10.0    inches  =  25.  4  cm. 

to         7.0    inches  =  17. 8  cm. 

0.  000  0254  cm. 

0.0000178cm. 
d  —  ~16.  25  inches  =  41.  2  cm. 

to  11. 5  inches  =  29. 2  cm. 

0.  000  0412  cm. 

0. 000  0292  cm. 

d  =  14. 8  inches  =  37. 6  cm. 

«'  =  0.  000  0376  cm. 


={ 


36.  4  inches  =  92.  5  cm. 

0.  000  0925  cm. 
16.  0  inches  =  40.  6  cm. 

0.  000  0406  cm. 


3. 5  inches  =    8.  9  cm. 

to     7.  0  inches  =  17.  8  cm. 

f  0.  000  0089  cm. 

\  0.  000  0178  cm. 

4.  25  to  60  inches  =  10.  8  to  152.  4  cm. 
Contents  of  cylinder   usually  dry  or 
nearly  so. 


DESCRIPTION  OF  METHOD  (A)  AND  APPARATUS. 

The  ideal  aimed  at  in  the  disposition  of  the  apparatus  was  to  obtain  a  concave  surface  of 
polished  silver  at  constant  temperature,  having  the  bolometer  strips  at  its  center  of  curvature, 
and  completely  filling  the  circular  openings  in  the  multiple  bolometer  screens  of  polished  metal. 
Eadiations  proceeding  from  the  bolometer  toward  the  concave  mirror  (distant  about  125  cm.)  would 
then  be  directly  returned,  except  as  affected  by  absorption,  while  rays  from  any  objects  in  front 
of  the  mirror,  but  outside  of  the  cone  of  rays  from  the  bolometer  to  the  mirror's  edge,  could  not 
possibly  be  reflected  upon  the  bolometer. 

The  bolometer  being  at  the  bottom  of  the  deep  cylindrical  cavity  of  its  ebonite  case,*  pro- 
tected from  air  currents  by  internal  diaphragms,  and  further  shielded  by  the  multiple  metallic 
screens  already  mentioned,  it  was  arranged  to  transpose  the  volume  of  air  intervening  between 
the  mirror  and  the  outer  bolometer  screen,  and  to  substitute  volumes  of  hot  or  cold  air  so  rapidly 

*  See  Plate  2,  accompanying  Prof.  S.  P.  Langley's  article  "On  Hitherto  Unrecognized  Wave-lengths,"  in  Am. 
Journ.  of  Sci.,  vol.  132. 


29 

that  the  temperature  of  the  bolometer  should  remain  unaffected  save  by  the  feeble  radiation  of 
the  gas,  the  temperature  of  the  concave  mirror  being  expected  to  remain  appreciably  unchanged 
in  the  brief  interval  of  exposure,  owing  to  the  small  absorption  of  radiation  by  silver  and  the 
continual  circulation  of  water  within  the  metallic  walls,  as  will  be  now  described. 

The  mirror  was  made  of  silver-plated  copper,  so  as  to  be  both  a  good  conductor  and  a  poor 
radiator,  but  owing  to  the  thinness  of  the  copper  and  its  yielding  quality  it  was  found  difficult  to 
preserve  the  spherical  figure.  The  mirror  formed  the  central  portion  of  the  front  face  of  a  rectan- 
gular vessel  containing  water  at  the  temperature  of  the  room,  and  on  testing  its  figure,  certain 
small  portions,  as  viewed  from  the  position  of  the  bolometer,  were  found  to  reflect  light  from  a 
lamp  flame  placed  outside,  but  close  alongside  the  aperture  of  the  bolometer  screen.  It  was 
evident,  therefore,  that  some  of  these  distorted  surfaces  might  reflect  enough  radiation  from  the 
interior  blackened  walls  of  the  cases  containing  the  hot  and  cold  air  to  entirely  vitiate  the  result. 

It  was  recognized  from  the  start  that  the  radiating  power  of  a  gas  is  so  greatly  at  a  disad- 
vantage, compared  with  the  emissive  power  of  a  solid,  that  the  least  exposure  of  hot  or  cold  metal 
in  front  of  the  bolometer  would  give  thermal  indications,  which  might  very  easily  be  greater  than 
those  to  be  expected  from  the  short  air  column  available  for  experiment.  The  failure  to  obtain  a 
perfect  spherical  reflector  which  should  also  be  a  good  conductor,  without  going  to  greater  expense 
than  was  deemed  advisable,  led  to  a  partial  modification  of  the  original  plan  in  the  coating  of 
the  mirror  with  lampblack.  The  layer  of  soot  being  very  thin,  must  retain  (it  was  supposed) 
substantially  the  temperature  of  its  metallic  backing,  in  spite  of  its  being  a  good  absorbent  of 
radiation,*  while  the  greater  part  of  the  blackened  spherical  surface  remains  incapable  of  reflecting 
outside  rays  to  the  bolometer,  owing  to  its  shape,  except  in  a  weak,  diffusive  way,  and  the  specular 
reflections  from  the  small  distorted  areas  are  rendered  ineffective  owing  to  the  feeble  reflecting 
power  of  lampblack  and  the  obstruction  of  rays  reflected  from  silver  in  traversing  the  discon- 
tinuous particles  of  powdered  carbon. 

The  first  experiments  were  made  to  compare  results  with  silver  and  with  lampblack  for  a 
background,  in  order  to  get  a  knowledge  of  the  magnitude  of  the  errors  which  are  to  be  guarded 
against,  and  of  the  legitimate  radiations  at  our  disposal. 

The  movable  air  chambers  were  cylindrical  vessels  of  tin  plate,  8  inches  in  diameter,  and  36.4 
inches  long,  provided  with  diaphragms  of  circular  aperture,  6  inches  apart,  and  graduated  from 
an  opening  of  2  inches  at  the  end  next  to  the  bolometer,  to  one  of  7  inches  at  the  further  extremity, 
adjacent  to  and  circumscribing  the  mirror  face.  The  inner  surfaces  of  the  air  chambers  were 
blackened,  and  apertures  were  provided  at  the  middle,  and  8  inches  from  each  end,  for  the 
insertion  of  thermometers,  whenever  the  temperature  was  read.  The  bulbs  were,  of  course,  drawn 
outside  the  limits  of  the  radiating  space  during  actual  work.  The  air  cylinders  were  contained  in 
tanks  3  feet  long,  and  1  foot  square  in  transverse  section,  the  cylinders  projecting  slightly  at  either 
end,  and  being  unjacketed  at  these  ends,  but  being  otherwise  completely  surrounded  by  the 
contents  of  the  tanks,  which  contained  either  hot  or  cold  water,  or  a  freezing  mixture.  The  tanks 
were  mounted  on  a  rolling  carriage,  moving  between  guides,  and  could  be  drawn  to  an  accurately 
adjusted  stop  on  one  side  or  the  other,  so  as  to  bring  the  longitudinal  axis  of  either  air  chamber 
in  line  with  the  bolometer  and  the  center  of  the  mirror;  and  this  could  be  accomplished  by  the 
observer  at  the  galvanometer  by  pulling  a  cord  passing  over  pulleys  to  the  movable  carriage,  thus 
transposing  the  air  vessels,  while  simultaneously  observing  and  recording  the  galvanometer 
readings. 

The  outermost  aperture  of  the  bolometer's  multiple  metallic  screen,  1.15  inches  in  diameter, 
at  12.3  inches  from  the  instrument,  was  concentric  with  the  2-inch  aperture  of  the  near  end  of 
the  air  chamber  which  was  13.2  inches  from  the  bolometer,  and  since  the  angular  aperture  of  the 
opening  in  the  screen,  as  seen  from  the  bolometer,  namely  5°.35,  was  much  smaller  than  those  of 
the  air  chamber,  which  were  8°. 67  for  the  near  aperture,  and  8°.07  for  the  further  opening  in  front 
of  the  mirrior,  there  was  no  danger  that  any  portion  of  the  walls  of  the  air  chamber  could  be 
directly  observed. 

Since  in  shifting  the  air  chambers  to  and  fro,  the  larger  or  7-iuch  aperture  remained  always 

*How  far  this  supposition  is  invalidated  will  be  sho^vn  in  the  sequel. 


30 

nearly  in  juxtaposition  with  the  silvered  face  of  the  fixed  water  tank,  very  little  air  could  escape 
at  this  end,  and  that  which  entered  at  the  2-iuch  aperture  was  prevented  from  having  free  circula- 
tion by  the  internal  diaphragms.  It  was  found  that  with  an  excess  of  60°  C.,  the  excesses  of  either 
of  the  internal  thermometers  of  the  air  chamber  above  the  temperature  of  the  outside  air  seldom 
differed  from  the  mean  by  as  much  as  5  per  cent.  The  temperature  gradient  of  the  central  axis 
of  the  air  chamber  has  therefore  usually  been  quite  moderate. 

The  following  temperature  readings  for  a  single  day,  March  15,  1892,  are  given  in  proof  of 
this  statement : 

TABLE  15. 


Excess  of  hot  cylinder 

above     outside    air 
temperature    as    in- 
ferred from  the  mean 
of    the    three    ther- 

Mean variation  of 
three  internal 
thermometers. 

mometers. 

e>0. 

0  C.    Per  cent. 

67.8 

±  0.  6  =  0.  9 

70.1 

±0.8  =  1.1 

69.5 

±  0.  9  =  1.  3 

66.9 

±1.9  =  2.8 

65.0 

±  0.  4  =  0.  6 

61.0 

±1.0  =  1.6 

65.4 

±  2.  1  =  3.  2 

61.8 

±1.8  =  2.9 

60.7 

±0.8  =  1.3 

56.3 

±  1.4  =2.5 

There  being  no  constant  order  in  the  relative  excesses  of  the  three  thermometers,  their  mean 
has  been  adopted  as  the  average  temperature  of  the  air  column. 

CORRECTION  FOR   THE   MAGNETIC  EFFECT  OF  THE  APPARATUS  DURING  MOTION  IN  METHOD  (A). 

The  positions  of  stone  piers,  and  other  necessities  of  the  case,  compelled  the  placing  of  the 
principal  apparatus  in  a  position  where  the  shifting  of  its  iron  parts  feebly,  but  appreciably, 
affected  the  very  sensitive  galvanometer.  Comparisons  of  the  galvanometer  readings  in  extreme 
positions  of  the  two  air  cylinders  were  therefore  made,  under  otherwise  identical  conditions,  to 
obtain  the  magnetic  effect  upon  the  galvanometer,  due  to  the  movement  of  these  considerable 
masses  of  tinned  iron  at  an  average  distance  of  12  feet  from  the  magnetic  needle. 


Experiment  of  July  29,  1892. 

All  parts  of  the  apparatus  were  substantially  at  the  temperature  of  the  room.  No  conceivable 
cause,  therefore,  existed  for  any  temperature  deflection.  Moreover,  variation  of  the  thermal  con- 
ditions by  making  the  blackened  silver  screen  hot,  but  leaving  the  intermediate  air  cylinders  cool 
and  equal  in  temperature,  gave  practically  the  same  result,  though  obviously  a  less  trustworthy 
one,  since  it  is  difficult  to  maintain  the  temperature  of  the  hot  screen  constant. 

Exposures  were  made  by  alternating  west  and  east  cylinders — that  is,  by  bringing  the  central 
axis  of  each  cylinder  in  turn  into  the  line  of  collimatioii  of  the  bolometer.  To  eliminate  galva- 
nometer drift,  each  pair  of  readings  with  west  cylinder  in  line  was  compared  with  the  intermediate 
reading  with  east  cylinder  in  line. 


Temperature  of  west  cylinder  (near  thermometer), 
Temperature  of  west  cylinder  (middle  thermometer), 
Temperature  of  east  cylinder  (rear  thermometer), 
Temperature  of  east  cylinder  (middle  thermometer), 
Temperature  of  blackened  water-filled  screen, 


°  C 
29.3 
29.3 
29.0 
27.8 
27.8 


31 

TABLE  16. 


First  series. 

Second  series. 

West  cylin- 
der in  line. 

Mean 

west. 

East  cylin- 
der in  line. 

Deflection 
east. 

West  cylin- 
der in  line. 

Mean 
west. 

East  cylin- 
der in  line. 

Deflection 
east. 

div. 

div. 

101.2 

99.0 

97.3 

99.3 

102.8 

+3.5 

95.0 

97.0 

101.9 

+4.9 

98.0 

97.7 

102.0 

+4.3 

96.9 

96.0 

100.1 

+4.1 

98.2 

98.1 

101.0 

+2.9 

99.2 

98.1 

101.8 

+3.7 

96.1 

97.2 

101.0 

+3.8 

97.  0  i          98.  1 

101.5 

+3.4 

98.5 

97.3 

101.0 

+3.7 

96.6 

96.8 

102.0 

+5.2 

97.3 

97.9 

101.8 

+3.9 

97.9 

97.3 

101.3 

+4.0 

93.9 

95.6 

99.0 

+3.4 

96.4 

.       97.2 

100.7 

+3.5 

96.0 

95.0 

100.2 

+5.2 

95.9 

96.2 

100.9 

+4.7 

98.8 

97.4 

100.1 

+2.7 

94.2 

95.1 

98.5 

+3.4 

98.8 

98.8 

'    101.6 

+2.8 

93.7 

94.0 

98.0 

+4.0 

Mean, 

+3.62 

Mean, 

+4.09 

The  probable  errors  of  the  two  series  being  i  0.16  div.  and  ±  0.14  div.,  equal  weights  may 
be  given  to  them,  and  their  common  mean  applied  with  opposite  signs,  according  as  the  change 
of  position  is  from  west  to  east,  or  the  reverse,  whence  the  mean  magnetic  deflection  by  presenta- 
tion of  east  cylinder  =  +  3.86  div. ;  by  presentation  of  west  cylinder  =  —  3.86. 


OBSERVATION   OF   AIR   RADIATION   BY  METHOD    (A). 

The  radiation  measures  with  the  nrst  apparatus  follow.  The  sensitiveness  of  the  galvanom- 
eter during  these  experiments  remained  unchanged.  The  astaticism,  checked  from  day  to  day, 
continued  constant.  The  time  of  a  half  vibration  of  the  needle,  chronographically  determined, 
was  9.7  seconds. 

A  comparison  of  deflections  with  polished  silver  and  blackened  reflector  showed  that  the 
former  were  from  two  to  three  times  the  greater,  proving,  as  had  been  anticipated,  that  the 
reflections  from  the  distorted  surface  of  the  silver  were  larger  than  the  air  radiation  to  be 
measured.  It  is  only  necessary,  then,  to  consider  those  measures  in  which,  the  bolometer  being- 
directed  to  the  concave  blackened  surface,  the  alternate  interposition  of  hot  or  cold  columns 
of  air  has  given  small  but  consistent  positive  deflections  from  the  heated  air.  There  remains 
only  the  uncertainty  whether,  in  spite  of  the  backing  of  conducting  copper  and  water,  the  outer 
radiant  layer  of  the  lampblack  may  not  change  temperature  by  contact  with  the  hot  and  cold  air. 
This  point  will  be  considered  in  connection  with  the  results  of  other  methods. 

Each  interposition  of  hot  air  has  been  made  between  a  pair  of  cold  ones  whose  mean  is  taken 
for  comparison,  and  the  movements  have  been  regularly  timed  in  such  a  way  as  to  allow  the 
galvanometer  needle  just  time  enough  to  complete  its  swing,  11  consecutive  readings  on  the 
cold  air  and  10  intermediate  ones  on  the  hot  air,  forming  a  series,  as  in  the  example  at  constant 
temperature  in  Table  16. 


32 


Experiments  of  March  10,  1892. 
West  cylinder  heated. 
East  cylinder  surrounded  by  refrigerating  mixture  of  snow  and  salt. 

TABLE  17. 


Deflections  (hot). 

Before  first 

T>       . 

\    f+£*                                      A 

AT              A       4 

HT                                A 

series. 

series. 

.oLlDer  SeCOIHl 

aeries. 

Mi'.'iii  iirst 
series. 

i\i  PATI  seconil 
series. 

First 

Second 

series. 

series. 

div.           div. 

Temperature  of  bolometer 

15°.  OC. 

14-.  4  C. 

14°.  5  C. 

14°.  7  C. 

14°.  5  C. 

15.0 

13.4 

"             "  screen 

20C.  0  C. 

19C.  6  C. 

19°.  2  C. 

19e.80. 

19°.  4  C. 

17.3 

11.2 

"             "  room 

12°.  3  C: 

12°.  2  C. 

12°.  1  C. 

12°.  3  C. 

12°.  2  C. 

15.2 

15.8 

Pressure  of  atmosphere 

729.  0  mm. 

(AtO°  C.) 

729.0mm. 

729.  0  mm. 

12.9 

15.4 

Dew-point 

5°.  60. 

5C.6C. 

5°.6C. 

13.1 

14.4 

Pressure  of  water  vapor 

< 

6.  78  mm. 

6.  78  mm. 

12.9 

15.9 

Water  per  cubic  meter 

7.  03  grams. 

7.  03  grains. 

11.0 

16.5 

Temperature  of  hot  air 

57°.  1  C. 

54°.  2  C. 

48°.  8  C. 

55°.  7  C. 

51°.  5  C. 

17.1 

15.6 

"            "  cold  " 

—  12°.  2  C. 

—  11°.  3  C. 

—  9°.  50. 

—  11°.  8  C. 

—10°.  4  C. 

11.2 

15.4 

"           excess 

69°.  3  C. 

65°.  5  C. 

58°.  3  C. 

67°.  5  C. 

61°.  9  C. 

13.4 

13.1 

Mean  deflections 

13.91 

14.67 

The  probable  error  of  the  mean  of  the  first  series  is  i  0.51  div.,  and  of  the  second,  i  0.37  div. 
The  battery  galvanometer  stood  at  99  div.,  and  the  deflections,  reduced  to  the  standard  current 
(100  div.)  and  corrected  for  the  negative  magnetic  deflection  of  the  west  cylinder,  become- 
First  series :      (+  13.91  +  3.86)  4-  0.99  =  +  17.95  div. 
Second  series:  (+  14.67  +  3.86)  -^-  0.99  =  +  18.72    " 

The  mean  temperature  of  the  hot-air  column  was  39°.()  above  that  of  the  bolometer,  arid  the  cold 
air  was  25°.7  below  the  instrument.  The  mean  atmospheric  pressure  was  729  mm.  and  the  force 
of  water  vapor  6.78  mm.,  equivalent  to  a  layer  of  liquid  water  0.000  236  cm.  thick  in  the  absorbent 
column,  33.5  cm.  long. 

Experiments  of  March  15,  1892. 

West  cylinder  heated. 

East  cylinder  surrounded  by  cool  water  of  nearly  the  same  temperature  as  the  bolometer. 
Silvered  reflector  freshly  blackened  by  smoking  it  over  a  smoky  lamp  flame. 

TABLE  18. 


Ale&n  iii'ist 

Deflections  (hot). 

Before  nrst 
series. 

Between 
series. 

Alter  second 
series. 

series. 

M  r;iii  second 
series. 

First     i    Second 

series. 

series. 

div. 

div. 

Temperature  of  bolometer 

8°.  7  C. 

8°.7C. 

8°.7C. 

16.1 

13.6 

"  screen 

7°.9C. 

8°.  0  C. 

8°.OC. 

8°.OC. 

15.0 

12.7 

"   room 

4°.  4  C. 

5°.2C. 

3°.  1  C. 

4°.8C. 

4°.2C. 

18.2 

19.0 

Pressure  of  atmosphere 

738.  4  mm. 

(AtO°C.) 

738.  4  mm. 

738.  4  mm. 

14.2 

13.8 

Dew-point 

—  10°.  OC. 

—  8-.9C. 

—  7°.8C. 

14.2 

7.7 

Pressure  of  water  vapor 

2.  35  mm. 

2.  55  mm. 

15.7 

12.9 

Water  per  cubic  meter 

2.  57  grams. 

2.  78  grams. 

10.2 

13.4 

Temperature  of  hot  air 

73°.  9  C. 

72=.  1  C. 

68°.  1  C. 

73°.  0  C. 

70°.  1  C. 

10.2 

12.9 

"            "  cold  " 

+  7°.  9  C. 

+  7°.5C. 

+  6°.8C. 

+  7°.  7  C. 

+  7°.2C. 

12.1 

15.4 

'  '           excess 

66°.  OC. 

64°.  6  C.         61°.  3  C. 

65°.  3  C. 

62°.  9  C. 

17.5 

18.2 

Mean  deflections 

14.34 

13.96 

33 


The  probable  errors  of  the  mean  deflections  are  ±  0.61  div.  and  ±  0.60  div.  Battery  galva- 
nometer =  102  div.  Deflections  reduced  to  standard  and  corrected : 

First  series :      ( +  14.34  +  3.86)  4-  1.02  =  +  17.84  div. 
Second  series :  (  +  13.96  +  3.86)  -=-  1.02  =  +  17.47    " 

The  mean  atmospheric  pressure  was  738.4  mm.,  and  the  mean  force  of  water  vapor  2.45  mm., 
equivalent  to  a  liquid  layer  0.000  090  cm.  thick  in  the  length  of  the  absorbent  column  of  air. 

In  the  third  and  fourth  series,  the  tank  around  the  cold  cylinder  was  filled  with  a  mixture  of 
snow  and  salt,  giving  as  wide  a  range  of  temperature  as  the  structure  of  the  apparatus  would 
permit. 

TABLE  19. 


Deflections  (hot). 

\Twn    f  nil  r  til 

series. 

series.                series.                 series.                 series. 

Third         Fourth 

series.         series. 

div. 

div. 

Temperature  of  bolometer 
"            "  screen 

8°.7C. 
8°.OC. 

9°.3C. 
8°.OC. 

8°.9C. 
8°.OC. 

9°.  2  C. 

8°.  0  C. 

18.0 
15.2 

18.2 
17.8 

"            "  room 

4°.2C. 

5°.6C. 

6°.  3  C. 

4G.  9  C. 

6°.OC. 

21.3 

20.9 

Pressure  of  atmosphere 
Dew-point 

(Approximatel1 
—  3C.3C.         —8°.  1C. 

f-) 
—1-.  I  C. 

738  mm. 

16.3 
18.6 

21.3 
17.7 

Pressure  of  water  vapor 
Water  per  cubic  meter 
Temperature  of  hot  air 
"           "  cold  " 

3.  59  mm, 
3.  84  grams. 
69°.  6  C. 
—  15-\  2  C. 

3.64  mm. 
3.  90  grams. 
67°.  4  C. 
—15°.  Q  C. 

4.  22  mm. 
4.  48  grams. 
67°.  OC. 
—14-.  4  C. 

3.  62  mm. 
3.  87  grams. 
68°.  5  C. 
—15°.  1C. 

3.  93  mm. 
4.  19  grams. 
67°.  2  C. 
—  14°.  7  C. 

24.0 
21.5 
18.4 
16.9 

17.3 
21.9 
23.2 

18.8 

"            excess 

84°.  8  C. 

82°.  4  C.         81°.  4  C. 

83°.  6  C. 

81°.  9  C. 

19.9 

18.6 

Mean  deflections 

19.01 

19.57 

The  probable  errors  are  i  0.60  div.  for  the  third,  and 
the  corrected  deflections  are  — 


0.51  div.  for  the  fourth  series,  and 


Third  series  :     (+  19.01  +  3.86)  -r-  1.02  =  +  22.42  div. 

• 

Fourth  series:  (  +  19.57  +  3.86)  +  1.02  =  +  22.97    « 

The  mean  air  pressure  was  about  738  mm.,  and  the  mean  force  of  vapor  3.78  mm.,  equivalent 
to  a  liquid  layer  of  water  0.000  135  cm.  deep  in  a  length  of  33.5  cm. 

Experiments  of  July  29,  1892. 

Object:  The  measurement  of  radiation  from  warm  air,  containing  'considerable  water  vapor, 
for  comparison  with  results  obtained  in  cold,  dry  weather.  Also  a  determination  of  the  absorption 
of  this  radiation  by  glass. 

East  cylinder  the  bot  one,  the  magnetic  influence  of  moving  masses  being  therefore  the 
reverse  of  that  in  previous  measures.  West  cylinder  surrounded  by  melting  ice.  Silvered 
reflector,  forming  the  background,  freshly  coated  with  soot. 

The  first  and  fourth  series  are  comparable  with  previous  measures,  varying  only  in  the  higher 
range  of  temperature  and  the  larger  quantity  of  water.  In  the  second  and  third  series,  the 
aperture  of  the  bolometer  case  was  covered  by  a  pane  of  window  glass  3.15  mm.  thick,  which 
transmits  about  76  per  cent,  of  the  total  apparent  solar  radiation,  and  14  per  cent,  of  that  from  the 
moon,  and  which  is  practically  impervious  to  rays  of  greater  wave-length  than  4£  microns,  giving 
us,  in  the  absence  of  spectrobolometric  measures,  a  preliminary  approximation  to  the  region  of  the 
spectrum  in  which  the  radiation  lies. 
12812—  Bull.  G  -  3 


34 

TABLE  -20. 


Before  first  , 
series. 

After  second 

series. 

Alter  fourth 
series. 

Adopted  for 
1  and  2. 

Adopted  for 
':*  and  4. 

Temperature  of  bolometer 

32-.  OC. 

32°.  OC. 

32°.  0  C. 

"            "  screen 

29°.  7  C. 

29°.  8  C. 

30°.  OC. 

29°.  8  C. 

29°.  9  C. 

"             "  room 

32-.  6  C. 

32-.  OC. 

32°.  5  C. 

32°.  2  C. 

Pressure  of  atmosphere 

730.74mm. 

(AtO°  C.) 

731.76mm. 

731.0  mm. 

731.5  mm. 

Dew-point 

23°.  9  C. 

23°.  3  C. 

Pressure  of  water  vapor 

21.  63  mm. 

21.  63  mm. 

Water  per  cubic  meter 

21.  06  grams. 

21.  06  grams. 

Temperature  of  hot  air 

93°.  2  C. 

89C.  1  C. 

89-.  5  C. 

91-.  2  C.           89~-.3C. 

"             "  cold  " 

+6°.5C. 

+8J.2C. 

+8°.  2  C. 

+7C.4C. 

+10C.  6  C. 

"         excess 

86°.  7  C.          80-.  9  C. 

80-.  9  C. 

76°.  5  C. 

78°.  7  C. 

DEFLECTIONS  FROM  HOT-AIR  COLUMN.* 


First  series. 

Second  series. 

Third  series. 

Fourth  series. 

d  a'. 

div. 

div. 

(lir. 

21.1 

10.1 

3.8 

26.9 

18.5 

3.4 

2.8 

27.8 

25.0 

7.4 

4.5 

22.5 

23.6 

5.9 

5.3 

20.6 

24.8 

4.1 

6.4 

24.4 

26.3 

9.1 

4.7 

21.9 

29.0 

4.3 

6.0 

22.5 

24.0 

4.5 

6.2 

21.7 

24.0 

4.5 

6.4 

24.6 

29.3 

2.6 

7.0 

24,4 

Mean  deflections 

24.56 

5.59 

5.31 

23.73 

*  Series  1  and  4  without  glass,  2  and  3  through  glass. 

The  probable  errors  of  the  means,  in  the  order  of  the  series,  are  i  0.65  div.,  ±  0.57  div., 
±  0.31  div.,  i  0.53  div. ;  and  the  battery  galvanometer  reading  being  96.5  div.,  the  deflection  , 
corrected  for  the  positive  magnetic  deflection  of  the  east  cylinder,  and  reduced  to  the  standard 
current,  are — 

First  series :      ( +  24.56  —  3.86)  —  0.965  =  +  21.45  div. 
Second  series:  (+    5.59  —  3.86)  -  0.965  =  +    1.79    " 
Thira  series:     (+    5.31  —  3.86)  —  0.965  =  +    1.50    " 
Fourtu  series :  (+  23.73  —  3.86)  —  0.965  =  +  20.59    " 

The  glass  used  transmits 

31  per  cent,  of  radiation  of  wave-length,     1.9 


18    "       " 
8    "      " 


3.1 
4.3 


Not  over  2-0  of  the  radiation  from  a  surface  of  lampblack,  at  the  temperatures  with  which  we  are 
dealing,  lies  in  this  region  of  very  limited  glass  transmission.  Most  of  the  fraction,  indeed,  will 
be  near  the  longest  wave-length  mentioned,  and  0.1  is  a  fair  index  of  its  average  transmission  by 
glass,  so  that,  if  we  say  that  it  is  hardly  possible  for  2-5-0  of  the  rays  from  the  lampblack  back- 
ground to  escape  absorption  by  glass,  the  statement  is  justifiable.  If  the  deflection  of  about  li 
div.  through  glass  is  genuine,  it  must  be  of  atmospheric  origin.  As  the  absorption  of  glass  is 
a  discontinuous  one,  at  any  rate  in  this  part  of  the  spectrum,  it  is  possible  that  the  absorption 
of  a  linear  gaseous  spectrum  whose  lines  or  bands  do  not  coincide  with  those  of  glass,  may  be 
much  less  than  for  a  continuous  spectrum  like  that  of  lampblack,  and  that  8  per  cent,  transmitted 
in  the  present  case  may  represent  a  fraction  of  gaseous  radiation  either  of  shorter  wave-length 
than  4£  microns,  or  of  greater  wave-length  than  the  region  of  lampblack  emission,  comparatively 
unabsorbed. 

In  proof  of  the  statement  that  the  absorption  of  glass  is  discontiuous,  it  may  be  mentioned 


35 

that  rays  in  a  small  part  of  the  lampblack  spectrum  from  a  glass  prism,  in  the  region  near  2^, 
were  found  to  be  three  times  as  transmissible  by  glass  as  in  the  same  region  from  a  rock-salt 
prism,  showing  that  certain  rays  which  are  present  iu  the  rock-salt  prismatic  spectrum,  have  been 
entirely  cut  oft'  in  the  spectrum  from  the  glass  prism,  and  that  those  rays  which  remain  pass 
through  glass  with  comparative  freedom. 

The  mean  atmospheric  pressure  in  the  experiments  of  July  29,  was  731.3  mm.,  the  vapor 
pressure  21.63  mm.,  and  the  equivalent  layer  of  liquid  water  in  the  absorbent  air  column  was 
0.000  706  cm.,  that  in  the  radiant  hot-air  column  being  about  twice  as  great,  and  five  to  seven 
times  as  great  as  in  the  experiments  of  March  15.  If  the  greater  amount  of  water  in  the  summer 
air  has  increased  its  radiative  power,  the  deflections  in  series  1  and  4,  July  29,  ought  to  exceed 
those  in  series  3  and  4,  March  15;  indeed,  without  any  change  in  radiant  emissivity,  some  increase 
of  radiation  was  to  be  anticipated,  because,  although  the  temperature-excesses  were  smaller  in 
July,  the  range  was  on  a  part  of  the  temperature  scale  farther  from  absolute  zero,  and  where  the 
differential  radiation,  as  shown  in  the  figures  for  lampblack  (Table  21),  may  be  expected  to  be 
greater.  The  summer  deflections  are  actually  a  little  smaller,  indicating  that  the  radiation 
measured  has  been,  to  a  considerable  extent,  that  of  the  lampblack  background,  which  has  suf- 
fered greater  absorption  by  water  in  summer.  The  following  tables  exhibit  these  relations,  the 
last  columns  being  stated  in  absolute  radiant  units.  The  radiating  volume  of  air  has  the  form  of 
a  truncated  cone  whose  angle  is  5°.35,  the  length  of  the  frustum  and  depth  of  the  radiating  layer 
being  92.5  cm.,  the  diameter  of  its  smallest  section  3.1  cm.,  and  that  of  its  largest  and  most  distant 
section  11.8  cm.,  while  the  volume  of  the  frustum  is  4,510  cub.  cm.  The  measured  radiation 
approaches  the  half  of  what  might  be  expected  from  surfaces  of  lampblack  at  the  given  temperatures. 

TABLE  21. 


Date  and  series. 

Temperatures. 

Computed  lamp- 
black radiation  to 
a  hemisphere. 

Ratio  to  lamp- 
black radiation 
from  100°  to  0°  C. 
r 

Computed  lampblack 
radiation  through 
small  aperture. 
EI  X  r 

Cent. 
t 

Absol. 
T 

o 

o 

Radim. 

Sadim. 

March    10,1892  (1) 

56 
—12 

329 
261 

.0135J  C070 

.  0065]  ' 

3r~ 

0.  000  001  355 

(2) 

52 
—10 

325 
263 

.  0129  ) 

iooeer0063 

SH°° 

0.  000  001  214 

March    15,  1892  (1) 

73 

8 

346 
281 

.  0158  1  A,™ 
.0082f 

1T6='603 

0.  000  001  469 

(2) 

70 

343 

O»JA 

.0155)  0075 

75          "- 

0.000  001  450 

7 

280 

.  0080  1 

126 

(3) 

69 
—15 

342 

258 

.  0153  )      AAQA 

.  0063J"  0(J 

90         711 
12_6 

0.000  001  740 

(4) 

67 
—15 

340 

258 

.0150)  0087 

|l=.  690           0.  000  001  682 
126 

July       29,1892  (1) 

91 

7 

364 

280 

.0186)  mnfi 
.  0080/'  01 

™=.  841           0.  000  002  050 

(4) 

89 
11 

362 
284 

.01841  ninn 
.  0084J-  UJ 

126"—  '94 

0.000  001  935 

For  the  equivalent  water  depths  in  the  first  three  columns  of  the  next  table,  reductions  of 
water  vapor  in  terms  of  mass  (m),  stated  in  grams  per  cubic  meter,  have  first  been  made  from  the 
indicated  vapor  pressures  (p)  and  barometric  pressures  (B),  reduced  to  the  freezing  point,  using 
the  formula  — 


^ 


p 


0.000  8041 
1  +  0.003  670* 


where  t  is  the  centigrade  temperature  of  the  hot  or  cold  air  in  the  radiant  air  column.  These 
masses  have  then  been  multiplied  by  the  factor  (w)  in  Table  14.  The  liquid  depths  are  given 
in  millionths  of  a  centimeter. 


36 

TABLE  22. 


, 

Liquitl  water  in  — 

Date  and  series. 

Radiant  layer. 

Corrected 
deflection. 

Tempera- 
tine 

Measured  radiation. 

Absorbent 

excess. 

layer. 

Hot. 

Cold. 

Divisions. 

°  a 

Radim. 

March  10,  1892     (1)                 567 

200 

236 

17.95 

67.5 

0.  000  000  740 

(2)                 574 

223 

236 

18.72 

61.9 

0.  000  OOC  771 

March  15,  1892     (1) 

186 

230 

93 

17.84 

65.3 

0.  000  000  735 

(2) 

204 

250 

93 

17.47 

62.9 

0.000  000  720 

(3) 

291 

153 

130 

22.42 

83.6 

0.  000  000  924 

(4) 

317 

158 

140 

22.97 

81.9 

0.  000  000  946 

July     29,  1892     (1) 

1473 

754 

706 

21.45 

76.5 

0.000  000  884 

"               (4)                1480 

916 

706 

20.59 

78.7 

0.  000  000  848 

EXAMINATION   OF   PROFESSOR    HUTCHINS'  HYPOTHESIS   "  THAT   RADIATION   TAKES   PLACE  ONLY 
WHEN  THERE   IS  A  FALL  OF   TEMPERATURE  WITHIN   THE   LIMITS  OF   MOLECULAR  ACTION." 

In  a  research  oil  the  Radiation  of  Atmospheric  Air  (Am.  Journ.  of  Sci.,  vol.  43,  p.  357-363, 
May,  1892)  Prof.  C.  0.  Hutchins  endeavors  to  determine  the  effect  of  varying  the  thickness  of  a 
radiating  layer  of  air.  "A  flat  sheet-iron  pipe  was  made  100  cm.  long,  10  cm.  wide,  and  2.5  cui. 
thick."  This  pipe  was  supported  in  an  inclined  position  and  heated  by  Bunseu  burners.  "  The 
air  exit  was  from  a  pair  of  jaws,  one  fixed,  one  movable,  so  that  the  thickness  of  the  air  column 
at  its  escape  could  be  regulated  at  pleasure.  *  *  *  The  results  were  recorded  as  the  amount 
of  galvanometer  deflection  per  degree  of  t  —  V.  With  openings  less  than  1  cm.  no  difference  in 
the  amount  of  radiation  can  be  detected.  With  larger  openings  a  small  increase  is  observed." 


Opening,  0.5  1 

Deflection  per  degree,        0. 193        0. 195        0. 245        0. 259 

The  conclusion  drawn  is  "  that  radiation  is  very  largely  from  the  surface  of  contact  between 
the  hot  and  cold  air,  which  seems  to  indicate  that  a  heated  gas  absorbs  all  or  nearly  all  those 
rays  that  it  itself  emits,  and  that  radiation  takes  place  only  when  there  is  a  fall  of  temperature 
within  the  limits  of  molecular  actijn;/  (p.  363,  loc.cit.).  The  values  given  show  that  when  the 
air  aperture  was  enlarged  sixfold,  radiation  only  increased  in  the  ratio  of  259  to  193,  or  by  34  per 
cent. ;  but  it  seems  to  me  that  the  inferences  are  not  warranted.  The  uprushing  jet  draws  cool 
air  from  the  sides  and  mingles  it  with  the  hot  air,  and  the  effect  of  this  admixture  is  proportionally 
greater  in  a  narrow  jet,  so  that  until  the  aperture  is  considerably  greater  than  those  used  by 
Professor  Hutchins,  the  cooling  by  admixture  very  nearly  neutralizes  any  gain  from  greater 
depth  in  the  line  of  sight.  The  viscosity  of  air  prevents  a:i  indefinite  extension  of  the  mixing.  A 
jet  of  more  than  a  certain  depth  at  a  given  altitude  above  the  nozzle  will  have  its  temperature 
lowered  by  mixture  only  at  the  borders  of  the  ascending  air  column,  tfce  central  part  of  the  cross 
section  of  the  heated  air  'having  a  constant  te  nperature.  Except  for  absorption  of  its  own 
radiation  by  the  air  any  further  increase  of  depth  will  then  give  radiant  values  greater  in 
approximate  proportionality  to  the  thickness  of  the  layer.  Professor  Hutchins  appears  to  have 
been  deceived  by  an  eye  observation,  which  he  describes  on  page  359  (Joe.  cit.).  "By  burning 
touch  paper  at  the  bottom  of  the  tube,  the  lamps  beneath  being  lighted,  the  shape  of  the  column 
of  air  from  the  nozzle  can  be  inspected  at  leisure  by  reason  of  the  dense  smoke  that  issues  with  it, 
and  by  filling  the  throat  of  the  nozzle  it  can  be  given  such  a  shape  that  the  column  of  heated  air 
will  preserve  uniform  dimensions  for  a  considerable  distance  from  its  exit."  On  the  strength  of  this 
observation  of  a  uniformity  of  cross  section  in  the  ascending  air  column,  a  constant  velocity  and 
identical  composition  of  the  jet  "for  a  considerable  distance  from  its  exit"  seems  to  have  been 


37 

inferred;  but  this  is  incorrect,  since,  as  I  shall  show,  the  thermal  gradient  of  a  cross  section  of 
the  air  column  is  not  only  not  a  single  valued  quantity  in  a  given  instance,  but  the  form  of  the 
gradient  varies  with  the  aperture  of  the  nozzle,  and  this  implies  variation  of  velocity  and  more  or 
less  admixture  of  cool  air. 

DESCRIPTION   OF   METHOD   B. 

Method  A  having  been  discredited,  or  at  least  having  come  under  suspicion,  no  attempt  was 
made  to  extend  it  to  air  columns  of  other  dimensions;  but,  instead,  the  bolometer  was  pointed  to 
a  cold  screen  entirely  separated  from  the  hot  air  which  issued  from  an  effluent  chamber  of  wood 
(fig.  3)  placed  over  the  hot-air  flue  from  the  furnace,  whose  register  could  be  opened  or  closed  by 
pulling  cords. 


.in.       ,-uv 

*  7 


£ 


/* 


vn. 


n 


—~f— 
<      7m  ^ 

/  x  *^t' 

-   /O                      -  ^, 

A 

~              • 

LI        fa        '  \         i 

^ 

; 

/  '                                 *v  \ 

16 

The  aperture  through  which  the  hot  air  issues  has  a  length  of  16  inches  (40.6  cm.)  and  a 
breadth  of  anything  less  than  7  inches  (17.8  cm.),  as  determined  by  the  position  of  a  sliding  panel. 
By  rotating  the  wooden  casing  through  90°,  either  the  longitudinal  or  the  transverse  axis  of  the 
aperture  can  be  made  parallel  to  the  line  of  sight,  giving  different  depths  of  radiating  air  without 
altering  the  section  and  general  condition  of  the  air  stream.  By  means  of  the  sliding  panel  both 
the  depth  and  sectional  area  of  the  air  stream  may  be  varied. 

The  hot  air  within  the  wooden  effluent  chamber  does  not  entirely  escape  upon  shutting  the 
register.  The  temperature  within  the  aperture  was  17°.6  higher  than  that  of  the  air  in  the  line  of 
sight,  4  inches  (10.2  cm.)  above  the  aperture,  when  the  register  was  closed;  but  with  the  register 
open,  the  strong  current  of  hot  air  maintained  a  uniform  temperature  in  the  vertical  direction, 
although  there  was  a  considerable  thermal  gradient  in  the  horizontal  direction  along  the  trans- 
verse axis. 

Experiments  of  February  23,  1893. 

The  bolometer  was  placed  18  inches  (45.7  cm.)  from  a  vertical  line  through  the  center  of  the 
aperture.  When  the  aperture  (16  by  6  inches)  was  end-on,  the  cone  of  rays  included  the  diameter 
of  the  air  vein  in  the  most  distant  section.  The  temperature  of  the  air  around  the  bolometer 
strips,  as  determined  by  a  thermometer  bulb  inside  the  bolometer  case,  was  10°.8  0.  at  the  begin- 
ning, and  9°.8  at  the  close.  Successive  readings  of  the  temperature  of  the  air  of  the  room  at 
intervals  of  some  minutes  were  4°.3,  4°.5,  5°.0,  4°.3,  4°.o.  The  temperatures  on  which  the 
deflections  depend  are  those  of  the  air  in  the  line  of  sight.  Three  thermometers  were  placed  in 
the  longitudinal  axis  of  the  aperture:  (a]  3  inches  from  its  farther  end  and  5  inches  from  the 
center,  (b)  at  the  center,  and  (c)  3  inches  from  the  nearer  end.  The  temperature  within  the 


38 


aperture  (register  shut)  was  24°.0.    The  thermometers,  elevated  into  the  line  of  sight,  uaa  a  mean 
temperature  of  6°.4  which  is  that  of  the  cold  air. 
In  the  hot  air,  the  readings  were — 


FIRST  SERIES. 

o 

o 

(a)  55.  8 
(6)  56.2 
(c)  56.  0 

Excess, 

49.4 
49.8 
49.6 

57.0 
59.2 
50.5 


SECOND  SERIES. 
Excess, 


50.6 
52.8 
44.1 


Mean  excess,          49.  6 


Mean  excess,          49.  2 


The  thermal  gradient  of  the  transverse  diameter  of  the  air  vein  is  represented,  on  the  average, 
by  the  following  series : 

49° 

46°        46° 

30°  30° 

15°  15° 

0  Excesses.  0 

The  thermometers  were  here  an  inch  apart. 

The  average  temperatures  of  successive  sections  on  either  side  of  the  longitudinal  axis  are : 
47°.5,  38°.0,  22°.5,  7.°5;  and  as  the  line  of  sight,  with  side  presentation,  penetrates  all  of  these 
layers  equally,  the  mean  temperature  of  the  radiant  air  in  the  second  experiment  is 

(47.5  _|_  38.0  +  22.5  +  7.5)  -=-  4  =  28°.9  C. 

In  determining  the  mean  temperature  for  the  end-on  presentation  of  the  first  experiment,  no 
great  refinement  of  computation  is  needed,  and  the  section  maybe  roughly  summarized  by  fourths, 
as  indicated  in  fig.  4. 


__ 

„  _  ~-  ~* 

__----• 

" 

7 

61^ 

—  —  -.  _____ 

-----. 

^ 

——-______ 

_£ 

16  im&fies 

%  4  (Plan) 


In  end-on  presentation  it  is  to  be  noted  that,  although  the  aperture  has  a  width  of  6  inches, 
the  heated  air  spreads  to  a  width  of  about  8  inches  at  the  level  of  the  line  of  sigh  t,  and  the  bolometer 
with  its  widest  angular  opening  takes  in  the  whole  of  this  width  at  the  distance  of  the  farther  end 
of  the  aperture,  as  shown  in  the  diagram. 

The  most  distant  quarter  of  the  air  vein  may  be  divided  into  eight  vertical  layers,  1  inch 
thick,  and  having  the  average  temperatures  just  given.  Cutting  these  layers  by  a  horizontal 
cylinder  which  includes  the  extreme  width,  the  areas  of  the  successive  transverse  sections,  count- 
ing from  the  axial  ones,  are: 

(1)  1.571  —  1.076=0.495 

(2)  1.076—0.614  =  0.462 

(3)  0.614—0.227=0.387 

(4)  0. 227 


Sum =4  ?r= 1.571 


To  obtain  the  mean  temperature  of  the  entire  section,  these  areas  may  be  treated  as  weights, 
giving  as  the  temperature  of  the  most  distant  fourth  of  the  air  vein — 

47.5  x  .495  +  38.0  x  .462  +  22.5  x  .387  +  7.5  x  .227 


=  320.8  C. 


1.571 


Similarly,  the  next  nearer  quarter  of  the  air  vein  may  be  considered  as  composed  of  six 
vertical  layers  of  the  central  hotter  region  cut  by  an  including  cylinder,  the  areas  of  successive 
sections  being — 

(1)  1.571  —  0.916  =  0.655 

(2)  0.916  —  0.343  =  0.573 

(3)  0.343 

The  mean  temperature  of  the  next  to  the  most  distant  fourth  is  then — 

47.5  x  .655  +  38.0  x  .573  +  22.5  x  .343 


1.571 


=  380.6  C. 


The  nearer  half  of  the  air  vein  may  be  assumed  to  consist  of  the  four  inner  vertical  layers 
and  the  areas  of  their  sections — 


(i) 

(2) 


1.571  —  0.614  =  0.957 
0.614 


The  mean  temperature  of  the  first  and  second  fourths  of  the  air  vein  is : 

fr  +  tt  _  47.5  x  .957  +  38.0  x  .614 
2  1.571 

=  430.8  C. 

* 

The  final  mean  is,  for  first  experiment — 

(32.8  +  38.6  +  43.8  +  43.8)  -4-  4  =  39°.7  C. 
The  observed  galvanometer  deflections  were  as  follows: 

TABLE  23. 


First  series  (aperture  end-on). 

Second  series  (aperture  sidewise). 

div. 

div. 

11.8 

4.0 

9.9 

1.7 

12.2 

3.1 

6.9 

2.9 

6.3 

0.0 

11.8 

3.8 

14.5 

2.3 

12.2 

1.5 

9.2 

4.2 

8.0 

5.3 

Mean 

=  10.  28  J-  0.  62 

Mean  =  2.  88^0.  34 

Multiplying  the  mean  temperatures  by  the  depths  of  the  radiating  air  layers,  assuming  these 


40 

to  be  proportional  to  the  dimensions  of  the  aperture  in  the  direction  of  the  line  of  sight,  the  com- 
puted air  radiations  and  their  ratio  are — 

(1)  16X39.7  =  635.2]  173.4 

(2)  6x28.9  =  173.4/         "635.2  — u-' 

The  observed  ratio  is — 

2.88  4-  10.28  =  0.280 

the  radiation  for  the  greater  depth  being  only  a  trifle  less  than  its  proportion  according  to  the 
product  of  depth  and  temperature. 

The  battery  galvanometer  read  96  div.  Reduced  to  standard  current  and  stated  in  absolute 
units  the  radiations  become — 

(Depth,  40.6  cm.)  Eadiation  =  10.71  div.  =  0.000  000  545  radim. 

(      «      15.2  cm.)  «         =    3.00  div.  =  0.000  000  153      » 

For  comparison  with  the  results  of  the  previous  method,  these  deflections  have  to  be  reduced 
to  the  smaller  aperture  by  dividing  by  8.96,  giving — 

(Depth,  40.6  cm.)  Eadiation  =  1.20  div.  =  0.000  000  049  radim. 

(     "       15.2  cm.)  "         =  0.33  div.  =  0.000  000  014      « 

With  a  depth  of  92.5  cm.  and  an  excess  of  65°,  assuming  proportionality  of  radiation  to  depth 
and  temperature  combined,  an  assumption  which  now  seems  justifiable  in  this  first  approximation, 
we  might  anticipate  a  radiation  of — 

GO   K  QK 

0.000  000  049  x  jj^  X  |0  =  0.000  000  181  radim. 

• 

The  measured  radiation  by  Method  A  (Table  22)  being  about  four  times  as  great  as  this,  we 
must  conclude  that  something  like  three  parts  of  the  observed  radiation  in  Method  A  were  due  to 
an  excessively  thin  layer  of  warm  radiating  lampblack,  with  a  small  amount  diffusively  reflected 
by  lampblack,  and  only  one  part  to  the  hotter  air. 

The  condition  of  the  air  in  the  experiments  of  this  date  was:  Barometer,  724  mm.;  dew-point, 
—  5°.3  C.,  corresponding  to  a  vapor  pressure  of  3.09  mm.,  or  to  3.34  grams  of  water  per  cubic 
meter.  By  Table  14  this  represents  the  following  depths  of  liquid  water  in  the  end-on  presenta- 
tion &i  and  the  sidewise  presentation  b-2 — 

cm. 
fci,  absorbent  layer  =  0.000  085 

radiant         "     =  0.000  135  (cold) 
"  "      =  0.000  118  (hot) 

Z>2,  absorbent  layer  =  0.000  127 

radiant        "      =  0.000  051  (cold) 
«  «      =  0.000  046  (hot) 

Experiments  of  February  25,  1893. 

The  bolometer  was  placed  15  inches  (38.1  cm.)  from  a  vertical  line  through  the  center  of  the 
aperture  whose  width  was  increased  to  7  inches  (17.8  cm.),  giving  a  hot-air  column  a  little  over 
9  inches  wide  at  the  level  of  the  line  of  sight. 


41 

The  longitudinal  axis  of  the  aperture  in  the  end-on  position  lying  east  and  west,  thermometers 
were  placed  at  the  level  of  the  line  of  sight— 

(a)  in  the  longitudinal  axis  of  the  air  column  8  inches  E.  of  center. 

tfo\    u      u  u  ct     u      u  u  Q        a        «      u        a 

fc\    a     a  u  u     u      u  u  3        u        a     u        a 

(d)  "    "  "  <;    "     "  "         at  the  center. 

(e)  2$  inches  north  of  longitudinal,  1  inch  east  of  transverse  axis. 

To  test  the  effect  of  the  hot  air  remaining  in  the  effluent  chamber  after  the  register  was  closed, 
the  thermometers  were  read  with  the  aperture  alternately  open  and  closed  by  a  board  cover. 

Aperture  open.  Aperture  closed. 

o  o 

(6)  8.0  6.3 

(c)  9.1  7.8 

(d)  8.6  7.0 

(e)  6.9  7.2 

I  have  adopted  for  the  temperature  of  the  cold  air  (register  closed,  but  aperture  open)  — 


The  temperature  of  the  bolometer  case  was  10°.S,  and  the  mean  temperature  of  the  air  of  the  room 
was  6°.0. 

The  thermometer  readings  in  the  hot-air  column  in  the  first  series  were: 

o 
(a)        62.8^| 

68  8  f  66°.4  =  mean  of  temperatures  at  east  end  of  longitudinal  axis. 

(d)  71.0J 

(e)  44.2 

In  the  next  series,  thermometer  (e)  was  transferred  to  a  point  in  the  longitudinal  axis,  8  inches 
west  of  center  — 


East 


(a)        45.(T 
(6)        73.4 


(c)        74.2  VMean  of  temperatures  in  longitudinal  axis  =  66°.8. 
Center    (d)        74.8 
West      (e)        66.6 

Thermometers  (a)  and  (e)  in  this  series,  being  near  the  point  where  the  thermal  gradient 
becomes  very  steep,  are  liable  to  vary  considerably  for  a  slight  displacement  of  the  vertical  axis 
of  the  ascending  air  column. 

The  last  two  series  of  temperature  readings  have  been  taken  with  thermometers  in  the 
transverse  axis  of  the  hot-air  column  in  positions  at  even  inches  from  the  center — 

Third  series.  Fourth  series. 

o  o 

3  inches  north  of  center        27.4  32.0 

2       "          "      "       "  63.0 

1  inch          "      "       "  ....  70.2 

Center  70.2  70.5 

1  inch  south  of  center  67.7  68.1 

2  inches  "      "       "  63.0 

3  "       "      "       "  47.8  

4  "        "      "       "  23.8  

5  "       "      "       "  13.4 


42 

These  thermal  sections  show  a  spreading  of  the  hot  air,  and  its  mixture  with  the  surrounding 
cold  air  for  an  inch  or  so  outside  the  original  dimensions  of  the  stream  at  the  aperture  of  the 
effluent  chamber.  The  heat,  however,  is  nearly  uniform  for  about  12  inches  in  the  center  of  the 
longitudinal  axis.  Fig.  5  exhibits  these  thermal  gradients  to  the  eye — 

Abscissae  =  distances  from  center  of  air  stream. 
Ordinates  =  temperature-excesses  (C.). 
1  and  2      =  series  along  longitudinal  axis. 
3  and  -4      =      "         "      transverse        " 


10       8 


ITl 


The  average  thermal  gradient  of  the  transverse  axis  of  the  hot-air  column  may  be  represented 
by  the  following  series : 

63° 

61°        Clo 
550  550 

30°  30° 

10°  10° 

0  Excesses.  0 

The  average  temperatures  of  successive  sections  on  either  side  of  the  longitudinal  axis  are, 
62°,  58°,  42°.5,  20°,  5°;  and  the  mean  temperature  of  the  radiant  air,  when  the  line  of  sight  agrees 
with  the  transverse  axis  of  the  air  column,  is — 

(62  +  58  +  42.5  +  20  +  5)  4-  5  =  37°.5  C. 


43 

Fig.  6  shows  the  disposition  of  bolometer,  aperture,  and  air  stream  in  the  end-on  presentation. 

In  getting  the  meau  temperature  for  this  position,  a  small  allowance  has  been  made  for  the 
lack  of  symmetry  of  the  air  column.  Dividing  the  air  stream  into  a  nearer  and  a  more  distant  half, 
the  mean  temperature  of  the  former  may  be  taken  as  61°.  The  more  distant  half  varying  from  a 


• 


__  __  4.  -- 


I 


V 


Jig.  6  (Plan) 


mean  of  61°  at  the  nearest  section  to  40°  at  the  most  distant  section,  a  rough  approximation  gives 
its  mean  temperature,  in  the  part  cut  off  by  the  cone  of  rays,  as  55°,  the  final  mean  for  the  hot 
air  radiating  to  the  bolometer  being  58°  C. 

Two  widths  of  aperture,  7  and  3%  inches,  were  used  with  side  presentation.  In  the  end-on 
position  the  breadth  of  the  aperture  was  constantly  7  inches  and  the  length  16  inches.  The 
observed  galvanometer  deflections  follow: 

TABLE  24. 


First  series,  end 

Second  series, 

Third  series,  end 

Fourth  series, 

on  (16  inches). 

side  (7  inches). 

011  (16  inches). 

side  (3J  inches). 

(Uv. 

div.                         div.      •                    div. 

5.2 

4.2 

7.6 

1.7 

9.7 

4.6 

9.7 

—1.9 

12.8 

3.8 

12.2 

0.8 

9.4 

3.2 

8.4 

1.9 

11.7 

2.3 

9.9 

0.0 

7.6 

2.9 

12.0 

1.0 

6.7 

2.5 

6.5 

0.6 

9.2 

4.  6                    13.  0 

0.6 

6.5 

3.  8                      4.  8 

2.7 

11.3 

2.  7                    10.  1 

1.5 

9.01^.56 

3.46^.21 

9.  42-J-.  59 

0.  89^.  25 

Observed  radiation  ratios. 


Depth,  16 
u 


inches  (40.6  cm.) 
7  inches  (17.8  cm.) 
3.5  inches  (  8.9  cm.) 


Deflection,  9.22 
"  3.46 
"  0.89 


Eatio,  1.000 
"  0.375 
"  0.097 


Assuming  the  radiant  depths  to  be  proportional  to  the  dimensions  of  the  aperture  parallel 
with  the  line  of  sight  and  the  radiations  to  be  proportional  to  these  depths,  computation  makes 
the  air  radiations  and  their  ratios  — 


(1)  and  (3) 
(2) 


16  x  58     =  928 

7  x  37.5  =  262.5 
3.5  x  37.5  =  131.3 


Ratio  =  1.000 

"      =  0.283 
"      =  0.142 


44 

The  battery  galvanometer  standing  at  99  div.,  the  reduction  to  standard  current  and  absolute 
units  gives — 

Depth  40.6  cm.        Eadiatiou  =  9.31  div.  =  0.000  000  474  radim 
"       17.8  cni.  "         =  3,49  div.  =  0.000  000  178      " 

"        8.9  cm.  '•          =  0.90  div.  =  0.000  000  040      " 

The  deflections  in  the  fourth  series  are  too  small  to  be  trusted.  As  showu  by  the  transverse 
gradient,  the  ascending  air  has  suffered  a  lateral  displacement  in  the  direction  of  the  transverse 
axis,  presumably  from  a  side  draft;  and  since  the  end-on  deflections  are  notably  smaller  than 
on  February  23,  and  relatively  smaller  than  the  corresponding  side  deflections  which  are  not 
influenced  by  the  displacement,  it  is  probable  that  the  temperature  allowance  made  in  the  preceding 
computation  is  insufficient  to  compensate  the  actual  variation  at  the  time  of  radiation  measurement. 
It  will,  of  course,  be  understood  that  the  observations  of  temperature  and  radiation  were  not 
synchronous,  although  made  in  immediate  succession.  Series  1  and  3  are  therefore  given  half 
weight  in  the  final  mean. 

The  condition  of  the  air,  February  25,  was  as  follows:  Barometer,  726  ram.,  dew-point,  — 1.9°  C., 
corresponding  to  a  vapor  pressure  of  3.98  mm.,  or  to  4.24  grams  of  water  per  cubic  meter.  By 
Table  14,  the  depths  of  liquid  water  in  the  various  air  layers  are — 


Eadiant  depth  40.6 


*«  17, 


Absorbent  layer  =  0.000  075 
Eadiant          "     =  O.Ouo  172  (cold) 
=  0.000  142  (hot) 
=  0.000  124 
=  0.000  075  (cold) 
=  0.000  066  (hot) 


Absorbent 

Eadiant 
u 


TABLE  25. 


.Radiation  of  hot  air  (for  small  aperture)  reduced  to  a  depth  of  1  meter. 


liadim. 
Feb.  23       (1)  0.  000  000  049  —  .  406  =  0. 000  000  121,  *  =  40 

(2)  0.000  000  014-^.152=0.000  000  092,  *  =  29 
Feb.  25  (1,  3)  0.000  000  043  —  .  406  =  0. 000  000  106,  *  =  58 

(2)  0.  000  000  016  —  .  178  =  0. 000  000  090.  t  =  38 


Radiation  of  air  at  mean  temperature-excess  of  40°  C.  (Depth  1  meter.) 


0. 000  000  121 
0. 000  000  127 
0. 000  000  073 
0.  000  000  095 

Mean  =  0.000  000  104  radim. 


DESCRIPTION  OF  APPARATUS  AND  METHOD  C. 

In  order  to  experiment  on  the  radiation  of  air  at  various  pressures,  and  to  be  able  also  to 
substitute  other  gases  in  the  place  of  air,  a  closed  vessel  was  needed.  Of  course  this  presupposes 
some  sort  of  window  transparent  to  the  gaseous  radiation,  but  both  the  window  pane  and  the  walls 
of  the  vessel  visible  through  the  window  will  contribute  their  own  rays,  and  these  must  be  capable 
of  being  certainly  distinguished  from  those  of  the  gas.  This  was  effected  by  making  the  window 
pane  of  rock-salt  and  letting  the  opposite  radiant  wall  be  a  movable  one,  formed  of  a  blackened 
copper  disk  attached  to  a  steel  rod  sliding  in  a  stuffing  box  at  one  end  of  a  large  iron  cylinder. 
By  pushing  the  rod  in  and  out,  the  length  of  the  radiant  air  column  could  be  changed  without 
varying  the  temperature  and  radiant  power  of  the  solid  parts.  The  disk  served  the  further 
purpose  of  a  stirrer,  by  the  vigorous  motion  of  which  it  was  hoped  that  the  temperature  of  the  hot 


45 

air  could  be  made  appreciably  uniform.  This  hope  was  only  partially  realized,  as  the  sequel  will 
show;  but,  although  it  would  be  possible  to  devise  a  more  efficient  apparatus,  the  very  errors  of 
this  one  have  proved  instructive,  and  the  final  results,  after  the  discussion  and  elimination  of  these 
errors,  are  believed  to  be  trustworthy. 

The  radiation  cylinder,  as  actually  made,  consists  of  an  iron  cylinder  of  12  inches  internal 
diameter,  60  inches  long,  weighing  250  pounds,  with  flanges  at  the  ends  projecting  outward  to  a 
width  of  2  inches.  Heavy  plates  of  cast  iron  are  bolted  to  the  flanges,  the  joints  being  luted  with 
red  rubber.  The  front  end-plate,  facing  the  bolometer,  carries  lugs  and  a  ring-piece,  with  clamping 
screws  by  which  a  rubber-faced  metal  ring  is  held  against  a  thick  plate  of  rock-salt  (thickness, 
1.98  inches  =  5.03  cm.;  diameter,  3.80  inches  =  9.65  cm.),  holding  it  against  a  rubber  ring  sur- 
rounding  the  2-inch  aperture  in  the  center  of  the  end-plate.  A  glass  plate  slides  over  the  outside 
of  the  salt,  when  not  in  use,  to  protect  it  from  moisture.  Preliminary  experiments  having  proved 
that  rock-salt  might  be  heated  to  175°  C.  and  presumably  much  higher  without  danger  of  crack- 
ing, if  it  were  shielded  from  currents  of  cold  air  and  any  sudden  changes  of  temperature,  but  that 
without  this  precaution  the  salt  was  almost  sure  to  crack,  the  circumference  of  the  cylindrical 
block  of  salt  was  wrapped  in  about  an  inch  of  cotton  wool.  The  large  masses  of  metal  (the  end 
plates  weigh  about  20  pounds  apiece)  prevent  any  sudden  cooling  of  the  solid  parts.  The  rear 
end-plate  being  pierced  by  a  central  aperture  carries  a  stuffing  box  through  which  a  half-inch 
rod  of  polished  steel  passes,  air-tight,  with  rubber  packing,  its  position  and  that  of  its  terminal 
disk  being  read  by  divisions  cut  on  the  rod.  The  movable  disk  of  blackened  copper  is  0.12  inch 
thick  and  11.85  inches  in  diameter,  leaving  an  annular  opening  with  an  average  width  of  0.075 
inch  through  which  the  air  rushes  when  the  disk  plays  to  and  fro.  A  thermometer  in  the  front 
part  of  the  cylinder  records  the  temperature  of  the  air,  and  the  disk  is  prevented  from  coming 
nearer  than  4.25  inches  (10.8  cm.)  to  the  front  plate  by  a  fixed  stop.  This  defines  the  shortest 
radiant  air  column  which  can  be  used,  the  longest  being  60  inches  (152.4  cm.). 

The  cylinder  is  heated  from  below  by  four  large  Bunsen  burners,  each  having  a  protractor 
stopcock,  reading  to  degrees,  for  the  ready  regulation  of  gas  flow.  An  outer  cylinder  of  sheet  iron 
serves  as  a  hot-air  jacket  to  the  inner  one.  Four  openings  below  in  the  outer  casing  admit  the 
flames,  and  the  same  number  above  permit  the  escape  of  combustion  products. 

An  air  pipe  at  the  side  connects  the  inner  cylinder  with  air-pumps  and  a  mercury  gage,  and 
a  second  air  pipe  leads  to  a  small  iron  side-cylinder,  or  heater,  provided  with  graduated  stopcocks, 
and  joined  to  a  series  of  drying  flasks,  generators  of  carbon  dioxide,  etc.,  according  to  the  needs  of 
the  experiment. 

The  apparatus  is  shown  in  plan  on  a  scale  of  1-12  in  fig.  7. 


7 


iS 


10  inches 


The  radiation  cylinder  has  an  approximate  volume  of  6,787  cubic  inches  =  111.3  liters,  and 
holds  about  144  grams  of  air  at  760  mm.  pressure  and  0°  C.,  containing,  if  unpurified,  nearly  0.14 


46 

gram  of  carbon  dioxide.  The  actual  atmospheric  pressure  during  the  experiments  was  usually 
from  730  to  735  mm. 

The  bolometer  is  carried  by  a  massive  stand  which  permits  accurate  adjustment,  and  holds 
the  instrument  with  a  solidity  which  can  not  be  improved.  The  mounting  of  the  great  cylinder 
in  the  first  experiment  was  not  so  firm,  but  it  was  afterwards  stiffened  by  braces  and  gave  no 
further  trouble.  The  entire  apparatus  stood  on  a  stone  pier. 

The  bolometer  case  was  protected  by  the  multiple  tin-plate  screens  of  small  aperture,  the 
outer  screen  being  2.46  in.  from  the  front  of  the  lead  ring  which  clamps  the  rock-salt  to  the 
end-plate.  In  Jamin's  "  Cours  de  physique,"  3e  ed.,  tome  3,  3e  fasc.,  p.  93,  is  an  allusion  to  a 
source  of  error  neglected  in  the  otherwise  very  careful  work  of  Melloui.  The  polished  rock-salt 
plate  reflects  to  the  bolometer  rays  from  a  small  annulus  of  the  protecting  screen,  but  the  effect  in 
my  observations  is  very  minute ;  first,  because  the  polished  tin  plate  does  not  absorb  radiation 
well  and  is  not  much  heated ;  second,  because  any  rays  which  the  screen  may  emit  or  reflect  are 
only  feebly  reflected  by  polished  rock-salt;  third,  because  the  angular  aperture  of  the  measuring 
instrument  is  small;  and  in  general,  since  the  gaseous  radiation  is  measured  by  finding  the 
change  due  to  motion  of  an  internal  disk,  the  effect  in  question  is  constant  at  a  given  temperature, 
and  without  influence  on  the  result. 

GENERAL  THEORY  OF  THE  APPARATUS  C. 

When  the  disk  in  the  heated  apparatus  is  moved  away  from  the  bolometer,  a  deflection  results 
which  is  made  up  (1)  partly  of  positive  gaseous  radiation,  (2)  partly  of  diminished  disk  radiation 
due  to  greater  gaseous  absorption,  (3)  in  part,  of  any  change  which  takes  place  in  rock-salt  radia- 
tion, which  may  be  either  positive  or  negative,  (4)  of  any  change  in  the  disk  radiation  due  to  its 
removal  to  a  part  of  the  cylinder  having  a  different  temperature.  This  also  may  be  either 
positive  or  negative,  and  is  quite  appreciable  if  the  cylinder  is  not  uniformly  heated,  for  instance, 
if  one  or  more  of  the  lamps  are  extinguished. 

For  the  present  purpose  (2)  need  not  be  separated  from  (1).  Absorption  simply  makes  the 
gaseous  radiation  appear  smaller.  Considering  (1)  and  (3),  the  rock-salt,  if  the  supply  of  heat 
were  equable,  would  tend  to  remain  at  a  lower  temperature,  as  a  whole,  than  the  gas  within  the 
cylinder,  because  the  outer  surface  of  the  salt  is  cooled  by  contact  with  the  outside  air,  and  its 
entire  substance  radiates  outwardly  through  a  wide  aperture.  Nevertheless,  since  the  thickness 
of  the  rock-salt  plate  is  great,  while  its  conductivity  and  radiative  power  are  small,  a  very 
marked  thermal  gradient  is  produced  within  the  salt,  and  in  actual  work  its  temperature  is 
always  changing.  The  air  gets  its  heat  chiefly  by  contact  with  the  hot  iron ;  the  salt,  on  account 
of  its  small  absorption  of  the  radiation  passing  through  it,  gets  its  heat  mainly  by  the  air 
convection ;  and  thus  the  temperature-changes  of  the  salt  continually  lag  behind  those  of  the  air 
and  iron.*  When  the  lamps  are  put  out,  the  air  and  iron  are  at  first  hotter  than  the  salt,  but  soon 
they  become  cooler  than  it.  The  withdrawal  of  the  disk  exposes  the  rock-salt  to  radiation  from 
the  walls  of  the  cylinder,  whose  mean  temperature  may  differ,  and  whose  radiative  power  certainly 
differs  from  that  of  the  disk,  and  also  to  contact  with  the  gas  swept  over  the  face  of  the  plate. 
If  the  gas  is  hotter  than  the  plate,  the  salt  is  heated  more  rapidly  than  before  by  this  increased 
contact  with  the  air  during  the  withdrawal  of  the  disk,  but  also  when  it  is  pushed  back.  This 
part  of  the  change  is,  therefore,  eliminated  in  the  same  way  that  the  effect  of  galvanometer  drift 
is  removed  by  combining  readings  made  before  and  after  exposure.  The  part  of  the  rock-salt 
temperature-change  due  to  variation  of  radiation  during  an  observation  is  not  thus  eliminated, 
but  is  too  small  to  be  measured. 

The  variations  in  the  radiation  of  the  copper  disk  (and  to  a  smaller  extent  those  of  the  rock- 
salt)  during  an  exposure  by  withdrawal  of  the  disk,  under  certain  extreme  conditions,  may  equal 
or  exceed  the  effect  attributable  to  the  combined  radiation  and  absorption  of  the  inclosed  hot  gas. 
Whether,  therefore,  there  is  any  appreciable  effect  from  the  heated  gas  under  the  peculiar 
conditions  of  these  experiments  with  the  radiation  cylinder  might  be  uncertain  were  it  not  for 
the  tests  to  be  described. 

*For  further  details  in  respect  to  rock-salt  radiation,  see  the  first  part  of  my  article  oil  "The  Probable  Eange 
of  Temperature  on  the  Moon/'  Astrophyaical  Journal,  vol.  8,  p.  199,  Nov.,  1898. 


47 

We  can  not  suppose  that  changes  in  the  thermal  condition  of  the  solid  parts  of  the  apparatus 
are  ever  entirely  absent;  but  since  the  sign  of  these  variations  of  temperature  is  reversed  in  passing 
from  heating  to  cooling  conditions,  it  might  be  supposed  that  a  mean  between  deflections  obtained 
with  a  heating  cylinder  and  those  from  a  cooling  one  would  be  due  to  gaseous  radiation  and 
absorption,  the  effect  of  any  possible  changes  in  the  copper  disk  canceling  out,  and  those  of  the 
rock-salt  being  eliminated  by  the  mode  of  exposure,  as  already  shown;  but  it  will  be  seen  subse- 
quently that  this  interpretation  of  the  results  is  not  permissible,  and  that  the  effect  of  another 
cause  of  discrepancy — that  of  imperfect  homogeneity  of  the  gaseous  radiating  column — must  be 
considered. 

When  the  radiation  cylinder  is  heating,  the  temperatures  of  the  well-stirred  air  being  taken 
as  abscissa,  the  observed  radiations,  plotted  as  ordinates,  fall  accurately  upon  a  straight  line, 
radiation  being  proportional  to  excess.  With  a  cooling  cylinder  the  radiations  are  very  much 
smaller,  and  fall  on  a  curved  line.  It  would  be  very  easy  here,  from  an  incomplete  or  an 
imperfectly  analyzed  experiment,  to  draw  erroneous  conclusions. 

The  wrought  iron  cylinder  (except  where  the  flame  plays  directly  upon  it),  by  virtue  of  its 
thermal  conductivity,  must  be  not  very  far  from  the  mean  temperature  of  the  hot-air  jacket  (which 
has  been  measured),  but  lagging  behind  somewhat  both  in  heating  and  cooling.  The  temperature 
of  the  air  within  the  cylinder  lags  still  more,  because  of  its  small  conductivity.  The  cylindrical 
surface  of  iron  to  be  heated  has  an  area  of  2,263  square  inches.  The  direct  impact  of  the  flame  is 
exerted  upon  not  more  than  T£F  of  this  surface,  and  the  play  of  a  flame  at  1,000°  to  1,800°  C.  heats 
this  portion  unduly,  a  considerable  area  of  the  floor  of  the  radiation  cylinder  having,  by  conduction, 
more  than  the  average  temperature.  Columns  of  hot  air  rise  within  the  cylinder  along  its  central 
axis  during  heating,  over  each  of  these  hot  places,  and  these  columns,  much  hotter  than  the  ineau 
temperature  of  the  air  within  the  cylinder  (which  mean  temperature  is  alone  given  by  the  ther- 
mometer), produce  the  larger  deflections  during  heating.  The  supposition  that  change  of  tem- 
perature of  the  rock-salt  has  anything  to  do  with  the  deflection  has  been,  shown  to  be  untenable, 
and  is  most  completely  negatived  when  it  is  known  that  the  total  radiation  of  the  salt  is  less  than 
that  represented  by  the  deflection  in  question,  while  the  temperature  of  rock-salt,  and  thence  its 
radiation,  changes  very  slowly.  Variations  of  temperature  in  the  copper  disk  in  its  two  positions 
may  produce  considerable  deflections,  but  only  under  extreme  conditions  which  are  not  those  of 
the  actual  experiment.  Substitution  of  a  blackened  asbestos  disk,  a  bad  conductor  of  heat,  in 
place  of  the  conductive  copper,  also  makes  little  difference  in  the  result  with  a  cooling  cylinder, 
unless  the  temperature  distribution  is  abnormal.  The  deflections  obtained  in  the  ordinary  work- 
ing can,  therefore,  only  be  due  to  the  changing  dimensions  and  temperatures  of  the  hot-air  columns 
within  the  cylinder;  and  the  fact  that  there  is  a  larger  radiation  at  a  given  mean  temperature,  as 
indicated  by  the  thermometer,  when  the  temperature  of  the  cylinder  is  increasing,  together  with 
the  observed  relation  between  the  rapidity  of  the  heating  and  the  amount  of  the  radiative  excess 
over  the  measurement  with  a  cooling  cylinder,  the  deviation  being  greater  the  more  rapid  the 
heating,  testify  that  the  radiation  conies  from  a  body  subject  to  the  internal  changes  and  irregular 
structure  produced  by  convection ;  and  an  effect  which  at  first  sight  may  seem  anomalous  becomes 
a  proof  that  the  radiation  observed  is  really  that  of  the  air,  and  is  not  due  to  any  change  in  the 
thermal  condition  of  the  solid  parts  of  the  apparatus  during  exposure.  In  passing  from  the  condi- 
tion of  a  heating  cylinder  to  that  of  a  cooling  one,  with  but  slight  change  of  average  temperature, 
there  is  a  continuous  fall  of  radiation,  that  for  the  stationary  point  being  less  than  for  increasing 
temperature,  but  more  than  for  falling  temperature. 

When  heated  from  below,  the  central  region  of  an  inclosed  fluid  is  occupied  by  ascending 
columns  heated  beyond  the  mean  temperature  of  the  mass,  while  during  cooling  the  central 
currents  are  cooler  than  the  average.  This  central  region  in  the  present  case  is  the  only  one 
observed  by  means  of  the  bolometer  whose  indications  do  not  give  the  average  radiation  of  all 
the  air  in  the  cylinder,  but  that  of  the  rapidly  moving  and  thermally  varying  portion  included 
within  the  central  cone  of  rays. 

The  composition  of  the  axial  radiating  air  column  when  heating  may  be  analyzed,  probably 
with  some  approximation  to  the  truth,  as  follows:  Suppose  that  nine-tenths  of  the  air  in  the 
horizontal  stretch  of  this  axial  line  have  a  temperature  of  90°  and  radiate  with  an  intensity  of 


48 

4  for  each  tenth,  or  36  in  all,  while  one-tenth  is  air  just  rising  by  convection  and  heated  to  250° 
by  contact  with  the  hot  iron.  The  radiative  power  of  this  tenth  may  be  taken  as  85,  and  the 
total  radiation  is  121  ;  whereas  the  radiation  of  a  body  of  air  at  mean  temperature 


will  be  about  68  on  the  same  scale,  and  the  observed  radiation  is  nearly  double  that  appertaining 
to  the  given  mean  temperature. 

When  the  disk  is  "in"  —  i.  e.,  at  its  nearest  approach  to  the  rock-salt  plate,  while  the  tempera- 
ture is  increasing,  the  thermometer  of  the  radiation  cylinder  is  partially  separated  from  the  larger 
part  of  the  interior  space  and  from  the  chief  source  of  heat  supply.  The  reading  of  the  thermometer 
is  therefore  lower,  since  the  ends  of  the  cylinder  cool  faster.  But  even  with  the  disk  out,  the  ther- 
mometer reading  is  too  low,  as  is  shown  by  a  rise  of  several  degrees  after  a  quick  movement  of  the 
disk  to  and  fro  several  times  when  the  heating  cylinder  has  not  been  recently  stirred.  After 
about  ten  minutes  of  cooling,  however,  with  less  frequent  agitation,  no  change  in  the  thermometer 
reading  occurs  after  stirring.  The  distribution  of  temperature  is  therefore  more  equable  during 
cooling.  The  thermometer,  after  vigorous  stirring  of  the  air,  records  its  true  temperature,  as  in 
the  use  of  the  sling  thermometer. 

In  order  to  get  the  thermometer  out  of  the  line  of  radiation,  it  had  to  be  lifted  a  little  above 
the  central  axis  of  the  cylinder.  Hence,  without  mixture  of  the  air  layers,  the  reading  should 
have  been  too  low  in  heating,  too  high  in  cooling.  (See  thermal  diagrams.)  The  last  error,  however, 
is  inappreciable,  and  I  think  we  may  see  why  from  the  following  considerations  :  When  heating, 
the  metal  at  the  bottom  of  the  cylinder  is  quite  hot;  that  at  the  top  much  cooler.  The  air  is 
heated  by  contact  at  the  bottom,  and  being  thus  lighter  and  in  unstable  equilibrium,  it  rises 
and  carries  heat  to  the  middle  space,  mixing  with  cooler  air  until  its  ascension  is  stopped  by  the 
top  wall,  and  great  diversity  of  temperature  prevails.  For  example,  internal  air  in  immediate 
contact  with  the  iron  top  and  bottom  walls  being  at  50°  and  250°,  respectively,  an  air  temperature 
of  90°  should  be  found  at  some  point  in  the  upper  half  of  the  air  space  when  the  mean  tem- 
perature of  the  entire  mass  of  air  is  110°,  ascending  thirds  of  the  air  being  on  the  average  150°, 
100°,  80°.  Stirring  may  then  cause  a  rise  of  20°,  as  has  actually  occurred,  and  streaks  of  air  as 
hot  as  200°  may  reach  the  central  line,  contributing  more  than  their  share  to  the  total  radiation 
on  account  of  their  relatively  greater  radiative  power. 

The  following  centigrade  temperatures  of  the  hot-air  jacket  of  the  radiating  cylinder  were 

observed  (temperature  rising;  : 

o 

Jacket:    At  the  top,  near  center  257 

"     "      "        "    end  250 

"     "  side       "       "  140 

"     "bottom"       "  56 

o 
Upper  half,  254  +  140  =  197 

2 
Lower  half,  140+    56  =    98  Mean  = 

2 

Temperature  of  air  within  the  radiation  cylinder  =  110°. 

A  hypothetical  vertical  thermal  section  of  the  air  in  the  cylinder  is  indicated  in  the  diagram: 


o 

Top  wall  of  cylinder 

50 

Internal  air                90°< 

loolno0 

150J 

Bottom  wall 

250 

49 

The  cooling  of  the  metal  after  the  lamps  are  extinguished  is  chiefly  from  beneath  by  convec- 
tion currents,  which  rush  upward  through  the  space  between  the  radiation  cylinder  and  the  outer 
jacket,  while  the  air  within  the  cylinder  is  cooled  by  contact  with  the  metal  at  the  top,  whose 
temperature  differs  less  than  before  from  the  bottom  temperature,  and  little  change  is  suffered 
by  the  air  from  contact  with  the  cooler  metal  at  the  bottom  on  account  of  the  feeble  conductivity 
of  air  and  stagnation  by  greater  density  there.  Thus  the  distribution  of  temperature  in  cooling- 
may  be  this:  Air  in  immediate  contact  with  iron,  110°  and  75°  at  top  and  bottom,  respectively. 
Air  temperature  by  ascending  thirds :  105°,  110°,  115°.  Mean,  as  before,  110°. 

The  following  temperatures  of  the  hot-air  jacket  were  observed  after  the  preceding  ones,  but 
with  a  cooling  cylinder,  all  of  the  lamps  but  one  (the  second  from  the  rock-salt)  having  been 
extinguished : 

Q 

Jacket-    At  the  top,  near  center  129 

"     "      "        "    end  117 

"     "  side      "       "  95 

"     "bottom"       «  56 

o 
Upper  half,  123  +  95  =  109 

2 
Lower  half,    95  +  56  =    75.5  Mean  =    92 

2 

Internal  temperature  of  radiation  cylinder  =  110°. 

A  hypothetical  internal  vertical  temperature  distribution  in  close  agreement  with  these 
observations  is  shown  in  the  diagram : 


Top  wall  of  cylinder  110 

Internal  air  112°-5{l}ojllO° 

105 1 
Bottom  wall  75 


Here  all  layers  of  air  have  nearly  the  same  temperature.  The  position  of  the  internal  ther- 
mometer is  of  little  consequence,  and  small  change  results  from  stirring. 

Curves  of  radiation  and  temperature  with  a  cooling  cylinder  pass  so  nearly  through  the  points 
of  observation  after  prolonged  stationary  temperature  that  no  great  error  will  be  committed  by 
assuming  the  cooliug  observations  to  be  correct  after  cooling  has  progressed  for  a  little  time. 

That  the  larger  radiations  during  rapid  heating  are  abnormal,  and  indicate  excessive  heating 
of  the  bottom  of  the  cylinder  and  of  the  lowest  layers  of  gas,  is  proved  by  the  fact  that  under 
these  circumstances  the  apparent  mean  temperature  of  the  gas,  on  putting  out  the  lamps,  does 
not  vary  much  during  many  successive  stirrings,  although  the  deflections  diminish  continually 
until  the  customary  reading  corresponding  to  that  temperature  and  uniform  distribution  of  heat 
is  reached,  after  which  the  thermometer  begins  to  fall  rapidly  and  the  radiation  to  diminish  accord- 
ing to  the  usual  law. 

Example:  Cylinder  containing  carbon  dioxide.  After  heating  for  several  hours  the  lamps 
were  put  out  and  readings  taken  during  initial  cooling.  Battery  galvanometer,  113  div.,  but  here 
all  deflections  have  been  reduced  to  standard  current.  Each  deflection  in  this  and  the  following 
experiments,  unless  otherwise  specified,  is  the  mean  of  five  concordant  readings. 

All  temperature-excesses  are  reckoned  from  the  temperature  of  the  bolometer,  there  being  no 
other  standard  possible  in  the  mode  of  exposure  followed,  and  are  given  in  centigrade  degrees. 
Pressure  in  closed  cylinder  varying  from  744  mm.  to  718  mm.,  mean  731  mm.  (reduced  to  freezing 
point).    Temperature  of  room,  30°.2;  of  bolometer,  35°.2;  dew-point,  13°.9  C. 
12812— Bull.  G 4 


50 
TABLE  26. 


Heating  rate  per  minute. 

Temperature. 

Excess. 

Radiation. 

0 

0 

o 

Divisions. 

Series  1  :                                              +0.  83 
Lamps  out 
After  3  nun.                                 —0.  13 
"     7     "                                    —0.73 
"    12     "                                     —  1.  10 

132.6 
133.  2  Max. 
133.0 
131.4 
125.5 

97.4 

98.0 
97.8 
96.2 
90.3 

+19.  2  (abnormal) 

4-15.7            " 
4-12.4            " 
4-  8.  7  (normal) 

Series  2  (after  further  heating)         ±      0        127.4 
Lamps  out                                                     136.  2  Max. 
After  5  miu.  cooling                    —  0.  36        135.  3 
"    10    "          "                           —1.23        126.9 

1 

92.2 
101.0 
100.1 
91.7 

4-16.5  (abnormal) 

4-14.5           " 
+  9.5  (normal) 

The  last  and  subsequent  readings  of  each  series  are  normal,  the  temperature,  as  indicated  by 
the  internal  thermometer,  diminishing  rapidly. 

A  similar  result  has  been  obtained  in  the  use  of  an  asbestos  disk,  but  here  other  causes 
assisted.  To  determine  what  change,  if  any,  would  take  place  if  the  radiative  disk  were  noncon- 
ducting, the  copper  had  been  covered  with  blackened  asbestos  on  the  side  facing  the  rock-salt 
window.  With  a  heating  cylinder  the  apparent  air  radiation  was  greater  when  the  nonconducting 
disk  was  used,  and  much  greater  when  only  the  two  central  lamps  were  lighted  and  the  ends  of  the 
cylinder  were  at  lower  temperatures  than  under  normal  conditions,  even  although  the  duration  of 
the  experiment  was  prolonged  until  a  stationary  mean  temperature  was  reached.  The  surface 
chilling  of  the  disk  in  the  forward  position — i.  e.,  nearest  to  the  rock-salt,  increased  the  deflection, 
and  the  effect  persisted  until  the  difference  of  temperature  between  the  middle  and  the  ends  of  the 
cylinder  ceased.  The  abnormal  results  at  maximum  temperature  and  during  initial  cooling,  while 
the  apparent  or  recorded  mean  temperature  is  nearly  stationary,  are  in  this  case  due  to  the 
combined  effect  of  vertical  and  horizontal  inequality  of  temperature. 

Example:  Cylinder  filled  with  air  at  atmospheric  pressure,  thoroughly  dried  by  phosphoric 
anhydride,  and  purified  from  carbon  dioxide.  After  heating  continuously  for  23  hours  the  recorded 
mean  stationary  temperature  was  68°.9.  The  two  middle  lamps  were  then  turned  up  for  1  minute, 
until  the  temperature  had  risen  to  71°,  when  the  lamps  were  extinguished. 

TABLE  27. 


Heating  rate  per  minute. 

Temperature.    ;     Excess. 

Radiation. 

0 

0                                                         0 

IHviiions. 

4-2.1 

70.0 

38.0 

4-8.0  (abnormal) 

Lamps  out 

71.0  max. 

39.0 

After  4  nun.  cooling  -j-0.  0 

71.0 

39.0 

4-7.  5            " 

"      8    "           "         40.0 

71.0 

39.0 

4-5.  8            " 

"     12    "           "        —0.12 

70.  8                        38.  8 

4-4.  6            " 

"     16    "           "        —0.28 

70.0 

38.0 

4-3.  9            " 

«    20   "           "         —0.10 

69.2 

37.2 

4-2.8  (normal) 

Here,  after  prolonged  but  unequal  heating,  20  minutes  of  cooling  were  required  to  give  the 
approximation  to  a  normal  value,  recorded  in  the  last  line,  the  first  reading  being  nearly  three 
times  too  large. 

The  preceding  example  was  obtained  after  all  parts  of  the  cylinder  had  become  well  heated, 
the  inequalities  of  thermal  distribution  being  comparatively  small.  The  next  experiments  show 
the  extraordinary  increments  produced  by  the  use  of  the  asbestos  disk  with  a  rapidly  heating 
cylinder.  The  air  within  the  cylinder  was  approximately  dry,  and  purified  from  carbon  dioxide. 
Two  middle  burners  were  lighted,  with  cocks  set  at  30  div. 


51 

TABLE  28. 


Heating  rate 
per  minute. 

Temperature. 

Excess. 

Radiation. 

o 

o 

o 

Divisions. 

+1.2 

62.4 

25. 

8 

+  8.4 

4-1.4 

72.5 

35. 

9 

+16.2 

+1.8 

80.3 

43. 

7 

+20.9 

+2.1 

90.0 

53. 

4 

+24.6 

+2.6 

100.3 

63. 

7 

+30.6 

+2.0 

108.9 

72. 

3 

+35.5 

The  deflections  are  here  four  to  six  times  as  great  as  those  with  a  cooling  cylinder. 
A  repetition  of  the  experiment  gave  the  results  in  Table  29. 

TABLE  29. 


Heating  rate 
per  minute. 

Temperature. 

Excess. 

Radiation. 

o                            c 

B 

Divisions. 

+3.U                 61.8 

28.2 

+  13.4 

+2.  4                70.  8 

37.2 

+17.3 

+4.0                81.0 

47.4 

+25.0 

+4.  2                90.  9 

57.3 

+26.1 

+2.  8               100.  2 

66.6 

+32.6 

+2.0 

110.  2 

76.6 

+37.7 

The  observations  may  be  represented  by  a  straight  line  passing  through  the  origin  and  a 
deflection  of  30  div.  at  excess  63°,  giving  a  mean  deflection  of  0.476  div.  per  degree  of  excess. 
The  ratios  to  the  deflections  of  the  cooling  curve  are,  as  before,  about  six  to  one  at  the  middle  of 
the  heating  curve,  where  the  rate  of  heating  is  greatest. 

The  asbestos  in  the  forward  position  radiates  to  the  cooler  iron  of  the  end-plate,  and  hence 
becomes  cooler.  When  withdrawn  to  the  rear  the  blackened  surface  of  the  asbestos  absorbs 
radiation  from  the  hot  interior,  and  is  also  heated  by  contact  with  hotter  gas;  but,  although  the 
copper  back  is  now  near  a  cooler  end-plate,  the  uoucouductivity  of  asbestos  prevents  any  influ- 
ence from  this  cause.  The  positive  differential  effect  is  added  to  the  true  gaseous  radiation.  The 
conductivity  of  copper,  and  the  more  equable  distribution  of  temperature  in  the  metal  walls, 
prevent  any  but  a  small  temperature-change  in  the  copper  disk  during  the  time  of  an  observation 
in  the  normal  working  of  the  heating  cylinder,  and  the  larger  deflections  with  heating  cylinder 
are  in  this  case  due  almost  entirely  to  inequality  of  gaseous  temperature,  as  is  shown  by  the 
closer  agreement  of  the  readings,  after  prolonged  heating  to  a  stationary  temperature,  with  those 
of  the  cooling  curve;  but  the  results  with  asbestos,  under  the  same  circumstances,  are  different. 
When  the  lamps  are  put  out,  the  distribution  of  temperature  in  the  cooling  iron,  after  a  time, 
becomes  nearly  uniform,  the  increase  of  200  or  300  per  cent,  in  the  apparent  gaseous  radiation  with 
stationary  mean  temperature,  due  really  to  temporary  chilling  and  heating  of  the  surface  of  the 
blackened  asbestos,  then  ceases,  and  the  values  of  air  radiation,  observed  with  a  cooling  cylinder, 
are  nearly  the  same  with  an  asbestos  disk  as  with  copper.  These  measures  may  therefore  be 
included  with  those  from  which  the  final  curves  of  air  radiation  are  derived.  The  abnormal  values 
which  have  been  purposely  obtained  by  varying  the  method  and  conditions  of  working,  are  only 
used  to  arrive  at  an  understanding  of  the  meaning  of  the  ordinary  results,  and  to  derive  some 
indication  as  to  their  reliability.  Many  things  which  were  puzzling  at  the  time  the  experiments 
were  made  are  now  clear  to  me,  and  I  hope  that  they  will  be  so  to  the  reader  who  has  the  patience 
to  follow  the  details  of  a  research  beset  with  difficulties  and  intricacies. 

The  following  experiment  with  the  blackened  copper  disk  exhibits  the  result  of  a  still  wider 
departure  from  normal  conditions,  and  bears  witness  to  the  necessity  of  some  of  the  precautions 


52 

which  were  taken  in  the  ordinary  use  of  the  apparatus.  In  heating  the  hot-air  jacket  around  the 
radiation  cylinder,  four  large  Bunsen  burners  are  customarily  employed,  their  positions  being  such 
as  to  secure  as  uniform  distribution  of  temperature  as  possible  within  the  cylinder  with  the  given 
means.  With  only  one  lamp  lighted,  the  effects  are  very  different,  according  to  the  position  of  the 
lamp.  When  the  single  lamp  was  at  the  end  farthest  from  the  rock-salt,  there  was  a  positive 
deflection.  The  mean  temperature  of  the  inclosed  air  had  been  so  regulated  that  it  was  falling, 
a  condition  ordinarily  attended  by  smaller  galvanometer  readings.  On  the  other  hand,  when  the 
single  lamp  was  at  the  rock-salt  end,  the  deflection  became  negative  with  a  heating  cylinder,  which 
ordinarily  gives  increased  readings. 

The  observation  follows:  Battery  current,  standard,  or  100  div.  Temperature  of  room,  26°; 
of  bolometer,  31° ;  dew-point,  11°.7,  corresponding  to  a  pressure  of  aqueous  vapor  of  10.23  mm.  or 
10.28  grams  per  cubic  meter,  and  to  an  equivalent  liquid  depth  of  0.000  387  cm.  in  the  absorbent 
layer. 

(a)  Fourth  lamp  (farthest  from  the  rock-salt)  lighted.  Burner  cock  set  at  30  div.  Temperature 
of  air  in  cylinder  read  immediately  after  vigorous  stirring: 

o 

Temperature  before  experiment    102.2 
"  after  "  97.8 


mean    =  100.0 
Excess  =   69.0 

Cooling  rate,  0°.8S  per  minute;  mean  differential  radiation  (disk  shifted  from  0.35  to  5.0  feet) 
-  +  7.80  div. 

(6)  First  lamp  (nearest  to  rock-salt)  lighted.    Burner  cock  set  at  35  div.    The  other  lamp  put  out. 

o 

Temperature  before  experiment,   104.  6 
Temperature  after  experiment,      108.  0 

Mean,     =  106.  3 
Excess,  =    75. 3 

Heating  rate,  0°.68  per  minute.  Mean  differential  radiation  (disk  shifted  as  before) 
=  -  1.34  div. 

Analyzing  the  component  sources  of  radiation  in  these  two  experiments,  and  neglecting 
absorption,  it  will  be  seen  that  in  (a)  the  copper  disk  was  getting  hotter  when  "out,"  and  was 
cooling  when  "in,"  or  at  the  end  next  to  the  rock-salt.  Its  thermal  change  had  the  same  sign  as 
the  hot-air  radiation  during  exposure  of  the  air  column.  The  front  walls  of  the  cylinder  were 
cooler  than  the  rear  walls,  and  cooler  than  the  copper  disk,  since  the  latter  evidently  suffered 
not  merely  a  halt  in  its  thermal  increment,  when  at  the  front,  but  a  decided  decrement  of  heat. 
Changes  in  the  temperature  of  the  rock-salt  contributed  to  the  combined  effect,  although  only  to 
a  slight  degree,  since  the  radiating  power  of  the  rock-salt  plate  was  but  one-fourth  that  of  blackened 
copper  at  the  same  temperature,  and  its  rate  of  change  very  slow.  When  the  warm  copper  disk 
was  pulled  out,  the  salt  received  radiation  from  the  front  walls  of  the  iron  cylinder,  far  from  the 
flame,  and  certainly  cooler  than  the  frequently  heated  copper,  also  less  powerfully  emissive. 
At  the  same  time,  cooler  descending  internal  convection  currents  played  upon  the  salt,  cooling  it, 
while  the  disk  was  getting  hotter.  The  thermal  change  of  the  salt  was,  therefore,  opposite  to 
that  of  the  copper. 

In  experiment  (6)  the  copper  disk  was  heated  at  the  front  and  was  cooling  while  at  the  farther 
end.  Its  change  of  radiation  was  therefore  of  the  opposite  sign  to  the  always  positive  radiation 
of  the  column  of  heated  air  (disk  out),  and  since  the  rock-salt  (disk  out)  was  exposed  to  the 
radiation  of  neighboring  walls  hotter  than  the  disk,  and  also  to  the  warmer  internal  convection 
currents  which  then  ascended  at  the  front,  the  thermal  change  of  the  salt  again  had  the  opposite 
sign  to  that  of  the  disk. 


53 

If  6c  =  the  variation  of  radiation  dependent  upon  thermal  change  in  the  black  copper  in  the  time 

of  exposure, 
<Ss  =  the  corresponding  variation  depending  upon  thermal  change  in  the  rock-salt,  modified  by 

its  own  absorption, 

r  =  the  mean  radiation  of  the  hot  air,  as  affected  by  self-absorption  and  assumed  to  be  con- 
stant, 

,r  =  the  transmission  of  hot  air  radiation  by  salt, 

y  =  the  transmission  of  the  radiation  of  black  copper  by  hot  air  and  salt, 
z  =  the  transmission  of  the  composite  radiant  beam  issuing  from  the  rock-salt,  exercised  by 
the  air  between  the  salt  and  the  bolometer, 
we  may  express  the  facts  of  these  experiments  thus : 

(a)  z  (xr  +  y  *c  —  6s]  =  +  7.80 

(b)  z(xr  —  y*c+  <5s)  =  -1.34 

The  change  of  radiation  of  the  rock-salt  in  a  quiescent  atmosphere  has  been  found  quite  inap- 
preciable during  the  time  of  exposure,  and,  although  somewhat  larger  under  strong  convection 
currents,  it  is  still  a  very  small  quantity;  but  for  illustration  it  may  be  included,  taking  6s  =  -^ 
ydc.  The  equations  give 

Constant  radiation  of  hot  air  xzr  =  +  3.23 

Variation  due  to  thermal  change  in  copper    yzSc  =  ±  4.6G 
Variation  due  to  thermal  change  in  salt  zds  =  ±  0.09 

The  total  radiation  of  black  copper,  rock-salt,  and  air  on  this  occasion  was  found  to  be  52.3 
div.,  the  excess  being  74°.    This  radiation  is  made  up  approximately  of — 
Radiation  of  black  copper,  transmitted  by  salt    T.9.3 
Radiation  of  air,  transmitted  by  salt  3.2 

Radiation  of  rock-salt  9.8 

.     The  rock-salt  plate  having  absorbed  one-fourth  of  the  original  radiation  from  the  interior,  the 
initial  deflections  before  absorption  may  have  been  : 

Blackened  copper    39.3  +  13.1  =  52.4 
Air  3.2+    1.1=    4.3 

The  indicated  radiation  for  the  blackened  copper  is  not  far  from  normal,  but  the  air  radiation 
is  only  a  little  over  one-third  of  that  obtained  by  the  usual  method,  no  doubt  because,  with  but 
one  lamp  burning,  only  a  part  of  the  air  is  effective,  the  distribution  of  temperature  being  far  from 
uniform,  as  the  variation  in  the  temperature  of  the  copper  disk  at  opposite  ends  of  the  cylinder 
also  proves. 

The  influence  of  self-absorption  of  its  own  radiations  by  a  gas  brings  into  play  another  factor 
which  changes  with  the  depth  of  the  gaseous  layer.  By  varying  the  play  of  the  disk  in  exposure, 
this  feature  may  be  partly  determined,  but  its  complete  elucidation  demands  apparatus  with  a 
great  range  of  dimensions. 

Paschen  ("Ueber  die  Emission  der  Gase,"  Wied.  Ann.,  Bd.  51,  S.  30,  1894)  finds  that  a  7-cm. 
layer  of  carbon  dioxide  absorbs  at  the  position  of  its  chief  band  "like  an  infinitely  thick  layer," 
and  that  the  absorption  of  aqueous  vapor  is  by  no  means  proportional  to  the  depth,  but  increases 
(at  wave  length  2.60 //)  from  GO  per  cent,  to  80  per  cent.,  when  the  depth  of  the  vaporous  layer 
varies  from  7  cni.  to  33  cm.  (loc.  cit.,  p.  12).  Hence,  gaseous  radiant  emission  is  not  proportional 
to  the  depth,  except  for  small  depths,  and  it  is  conceivable  that  there  may  be,  for  a  given  depth, 
some  temperature  of  the  gas  at  which  there  is  such  a  compensation  of  emission  by  absorption 
that  increase  of  thickness  will  not  affect  the  quantity — disk  radiation  plus  gaseous  radiation  plus 
gaseous  absorption.  In  fact,  Paschen's  fig.  8  (Taf.  1,  Wiefl.  Ann.,  Bd.  51)  shows  that  the  ratio  of 
gaseous  emission  to  gaseous  absorption  for  carbon  dioxide  changes  with  the  temperature,  and  the 
same  figure  permits  a  determination  of  one  point  on  a  curve  of  compensation  of  radiation  by 
absorption  for  this  gas. 

The  first  measurements  made  with  apparatus  C  were  to  find  the  relation  between  air  radiation 
and  depth,  and  to  these  we  may  now  pass. 


54 


METHOD    C.— EXPERIMENTS    IN   'WHICH    THE    DEPTH 

BEEN  VARIED. 


AND  PRESSURE    OF  THE  AIR  HAVE 


Each  of  the  two  air-pumps  diminished  the  pressure  in  the  cylinder  by  about  100  mm.  with 
the  first  20  strokes;  but  owing  to  the  slow  action  of  the  valves,  it  was  difficult  to  get  the 
final  pressure  below  50  mm.,  although  the  pumps  worked  well  enough  when  the  receiver  to  be 
exhausted  was  small.  In  addition  to  this  trouble,  there  has  always  been  some  leakage  at  low 
pressures — e.  </.,  in  one  experiment  where  the  air  temperature  did  not  exceed  100°  C.,  the  gage  at 
4h  27in  read  04.G;  at  5h  32™  the  reading  was  98.4  mm.,  the  pressure  having  risen  3.8  mm.  in  65™, 
or  0.0f>9  mm.  per  minute,  and  fresh  leaks  have  frequently  started  from  the  strain  of  heating. 
Consequently,  in  experiments  with  partial  vacuum,  it  has  been  necessary  to  work  rapidly,  and  in 
spite  of  drying  flasks,  some  aqueous  vapor  must  enter  through  leakage.  The  final  method  which 
overcame  this  difficulty  was  the  introduction  of  a  bowl  of  phosphoric  anhydride  within  the 
cylinder.  After  repeated  exhaustions,  allowing  air  to  flow  into  the  cylinder  through  a  series  of 
flasks  containing  porous  chloride  of  calcium,  experiments  were  commenced  January  25,  1893,  with 
air  nearly  dry,  but  still  containing  carbon  dioxide  in  the  usual  small  proportion.  Without  further 
announcement,  it  may  be  understood  that  in  all  the  readings  which  follow,  the  deflections  have 
been  reduced  to  standard  conditions  of  current  and  bridge.  The  change  is  usually  very  small, 
but  in  the  present  case,  with  battery  galvanometer  95  div.,  the  arrangement  of  the  bridge  was 
insensitive,  and  the  multiplier  is  2.0.  Mean  temperature  of  room,  20°;  of  bolometer,  25°;  dew- 
point,  12°.  2.  Pressure  of  aqueous  vapor,  10.57  mm.,  or  10.71  grams  per  cubic  meter.  The 
absorbent  layer  contained  enough  water  to  make  a  liquid  depth  of  0.000  403  cm.  The  disk  was  set 
at  even  feet,  but  the  initial  reading  with  which  comparison  is  to  be  made  is  that  of  the  shortest 
air  column,  0.35  feet.  The  measurements  were  made  at  both  ordinary  and  low  pressures. 

TABLE  30. 


Position  of  disk,  feet. 

0.35. 

1. 

2. 

3. 

4. 

5. 

Temperature. 

Excess. 

Pressure. 

Air  depth             {^ 

0 
0 

0.65 
19.8 

1.65 
50.3 

2.65 

80.8 

3.65 
111.3 

4.65 
141.8 

div. 

dir. 

div. 

div. 

dir. 

Deflections 

J       o 
1       o 

4.8 
6.0 

15.0 
15.8 

23.2 
24.0 

35.4 
32.6 

33.6 
32.0 

170° 
185.  5 

145- 
160.5 

95mm. 
723 

Mean  deflection 

0 

5.4 

15.4 

23.6 

34.0 

32.8 

Change  per  foot 

8.3 

10.0 

8.2 

10.  4 

—1.2 

The  two  series  in  this  table,  taken  at  pressures  which  vary  in  the  ratio  of  1 :  7.6,  are  almost 
identical.  The  discussion  of  this  at  first  sight  rather  startling  fact  is  reserved  for  a  subsequent 
section.  Except  for  the  last  foot  the  increase  of  radiation  is  proportional  to  the  depth.  In  view 
of  what  has  been  said  as  to  the  effect  of  unequal  distribution  of  temperature  it  might  be  suspected 
that  the  diminished  deflection  at  the  fifth  foot  comes  from  the  chilling  of  the  disk  by  proximity 
with  the  cooler  end-plate,  but  this  is  not  the  true  explanation,  as  the  next  example  demonstrates. 

TABLE  31. 

Cylinder  filled  with  dry  carbon  dioxide. 


Position,  feet. 

0.35 

1.                  2. 

1 

3. 

4. 

5. 

Temperature. 

Excess. 

Pressure. 

DePth                  {cm. 
Mean  deflection  (div.) 

000 

0.65         1.65 
19.  8         50.  3 
3.  5           7.  6 

2.65 
80.8 
10.4 

3.65 
111.3 
10.5 

4.65 
141.8 
10.2 

142C.  7 

125°.  8 

766mra. 

Change  per  foot 

5.4           4.1 

2.8 

0.  1 

—0.3 

55 


Two  things  are  shown  clearly  by  these  concise  tables,  namely,  that,  allowing  for  the  difference 
of  temperature,  the  apparent  radiation  of  carbon  dioxide  is  smaller  than  that  of  dry  air  at  tempera- 
tures not  exceeding  200°  0.  and  that  the  law  of  increase  of  radiation  with  the  depth  is  entirely 
different  for  these  two  substances.  To  make  the  last  point  quite  certain,  the  experiment  was 
repeated  with  dry  carbon  dioxide,  first  at  atmospheric  pressure  and  then  at  low  pressure.  These 
measures  are  given  in  full  as  an  example  of  the  mode  of  observation. 

February  17,  1894. 

Each  complete  observation  consists  of  three  successive  series,  of  ten  readings  each,  with 
differential  depths  of  carbon  dioxide  gas  of  4.G5  feet,  1.G5  feet,  and  again  4.65  feet,  the  middle 
series  being  contrasted  with  the  mean  of  the  extremes  to  eliminate  the  variation  from  change 
of  temperature.  Each  deflection  is  from  three  galvanometer  readings,  with  disk  in,  out,  and  in 
again,  and  is  complete  in  itself. 

Battery  galvanometer,  100  div.  Barometer,  734  mm,,  which  is  the  pressure  of  the  gas  in  the 
first  three  series.  Temperature  of  the  bolometer,  assumed  to  be  5°  hotter  than  the  reading  of 
the  dry-bulb  thermometer  placed  beside  the  bolometer  case.  The  temperature  of  the  bolometer 
is  taken  as  the  initial  or  comparison  temperature. 

At  llh  9m,  dry  bulb  =  63°.8  F.  =  17°.7  C. 
wet  bulb  =  55°.l  F.  =  12°.S  C. 

Difference,  8.7  +  4.4  (correction  for  uuveutilated  psychrometer  of  50  per  cent.)  =  13°.l  F. 
Dew-point,  38°  F.  Kelative  humidity,  0.38.  Temperature  of  radiation  cylinder  =  121°.0  C. 

TABLE  32. 

(Series  1.) 


Position  of  disk. 

In.               •  Out.                 In. 

Depth  of  gas  (fet-t). 

0.35                   5.0                   0.35 

div. 

105.1 

113.0 

104.1 

104.6 

+8.4 

104.1 

112.0 

105.2 

104.7 

+7.3 

106.1 

113.3 

103.4 

104.8 

+8.5 

105.0 

112.6 

108.0 

106.5 

+6.1 

100.0 

109.5 

103.0 

101.5 

+8.0 

103.0 

114.2 

105.8 

104.4 

+9.8 

106.1 

114.2 

105.8" 

106.0 

+8.2 

103.0 

112.1 

102.5 

102.8 

+9.3 

102.5 

111.4 

103.0 

102.8 

+8.6 

103.0 

112.2 

104.0 

103.5 

+8.7 

Differential  radiation  for  depth  (4.65ft.). 

+8.29 

At  II11  19m,  dry  bulb  =  65°.0  F.  =  18°.3  C. 
wet    "     =  560.0  F.  =  13°.3  C. 
Difference  =  9.0  +  4.5  (correction)  =  13°.5  F. 
Dew-point,  38°  F.    Relative  humidity,  0.37. 
Temperature  of  radiation  cylinder  =  126°.8  C. 

Mean  temperature  of  radiation  cylinder  (series  1)  =  123°.9  C. 
"  "  "  excess  (series  1)  =  100°.9  C. 

Mean  dew-point,  38°  F.  =  3°.3  C.,  or  pressure  of  aqueous  vapor  =  5.78  mm.,  corresponding  to 
6.04  grams  of  water  per  cubic  meter  of  air,  and  to  an  equivalent  depth  of  liquid  water  of  0.000  227 
cm.  in  the  absorbent  air  layer.  At  II1'  25m,  temperature  of  radiation  cylinder  =  133°.0  C. 


56 


TABLE  33. 

(Series  2.) 


| 

Position  of  disk.             , 

In. 

Out.                 In. 

Depth  of  gas  (feet). 

0.35 

2.0 

0.35 

die. 

100.0 

109.1 

103.8 

101.9 

+7.2 

99.2 

•     107.  7 

100.8 

100.0 

+7.7 

100.8 

109.6 

103.8 

102.3 

+7.3 

102.7 

111.1 

105.5 

104.1 

+7.0 

105.5 

114.0 

107.0 

106.3 

+7.7 

102.0 

112.0 

105.7 

103  9 

+8.1 

105.  9 

112.8 

108.0 

107.0 

+5.8 

97.8 

105.0 

98.2 

98.0 

+7.0 

98.2 

108.1 

102.6 

100.4 

+7.7 

102.6 

111.0 

101.9 

102.  3  • 

+8.7 

Differential  radiation  for  depth  (1.65  ft.). 

+7.42 

At  llh  33ra,  dry  bulb  =  65^.9  F.  ='18°.8  C. 
wet    "     =  570.0  F.  =  130.9  C. 
Difference  =  8.9  +  4.5  (correction)  =  13°.4  F. 
Dew-point,  40°  F.    Relative  humidity,  0.38. 
Temperature  of  radiation  cylinder  =  143°.2  C. 

Mean  temperature  of  radiation  cylinder  (series  2)  =  138°.l  C. 
"  "  "    excess  "          =  114°.5  C. 

Mean  dew-point,  39°  F.  =  3.9°  C.,  or  pressure  of  aqueous  vapor  =  6.03  mm.,  corresponding  to 
6.23  grams  per  cubic  nieter  of  air,  and  to  an  equivalent  depth  of  liquid  water  of  0.000  234  cm. 
in  the  absorbent  air  layer. 

TABLE  34. 

(Series  3.) 


Position  of  disk. 

In.                 Out.                 In. 

Vf  Ann    • 

T)   fl      t' 

Depth  of  gas  (feet). 

0.35 

5.0 

0.35 

div. 

105.  3 

116.8 

105.  0  | 

•    105.2 

+11.6 

105.0 

120.0 

106.8 

105.9 

+14.1 

106.0 

118.2 

107.1 

106.  6 

+11.6 

107.1 

119.0 

109.  0 

108.1 

+10.9 

101.6 

112.3 

101.0 

101.3 

+11.0 

101.0 

112.0 

101.8 

101.4 

+10.6 

101.8 

112.9 

102.  0 

101.9 

+11.0 

102.0 

115.0 

101.  8 

101.9 

+13.1 

103.0 

116.0 

102.8 

102.9 

+  13.1 

102.8 

115.0 

103.7 

103.3 

+  11.7 

Differential  radiation  for  depth  (4.65  ft.). 

+11.87 

57 

At  llh  43m,  dry  bulb  =  66°.8  F.  =  19°.3  C. 
wet     "     =  57°.4  F.  =  14°.l  C. 
Difference  =  9.4  +  4.7  (correction)  =  14°.l  F. 
Dew -point,  40°  F.    Eelative  humidity,  0.37. 
Temperature  of  radiation  cylinder  =  146°.7  C. 

Mean  temperature  of  radiation  cylinder  (series  3)  =  145°.0  C. 
»  "          .   «  excess  "          =  120°.9  C. 

Mean  dew-point,  40°  F.  =  4°.4  C.,  or  pressure  of  aqueous  vapor  =  6.24  mm.,  corresponding 'to 
6.50  grams  per  cubic  meter  of  air,  and  to  an  equivalent  depth  of  liquid  water  of  0.000  244  cm. 
in  the  absorbent  layer  of  air. 

The  cylinder  was  now  partially  exhausted  for  the  low-pressure  experiments. 

At  12h  6m,  dry  bulb  =  68°.0  F.  =  20°.0  C. 
wet     "     =  59°.0  F.  =  15°.0  C. 
Difference  =  9.0  +  4.5  (correction)  =  13°.5  F. 
Dew-point,  43°  F.    Eelative  humidity,  0.40. 
Temperature  of  radiation  cylinder  =  149°.9  C. 
Pressure  in  "  "        =85  mm. 


TABLE  35. 

(Series  4.) 


Position  of  disk. 

In.                 Out.                 In. 

Depth  of  gas  (feet). 

0.35                    5.0                  0.35 

div. 

93.8 

105.0 

93.2 

93.5 

+11.5 

93.2 

105.1 

90.7 

92.0 

+13.1 

90.7 

103.2 

91.5 

91.1 

+12.1 

91.5 

103.5 

92.2 

91.9 

+11.6 

92.2 

105.0 

92.0 

92.1 

+12.9 

92.0 

102.0 

91.2 

91.6 

+10.4 

91.2 

104.1 

88.0 

89.6 

+14.  5 

88.6 

102.1 

87.4 

88.0 

+14.1 

87.4 

101.1 

86.8 

87.1 

+14.0 

86.8 

99.  4             86.  1 

86.5 

+12.9 

Differential  radiation  for  depth  (4 

65ft.). 

+12.  71 

At  12h  12m,  dry  bulb  =  68°.S  F.  =  20°.4  C. 
wet    «     =  590.8  F.  =  150.4  C. 
Difference  =  9.0  +  4.5% (correction)  =  13°.5  F. 
Dew-point,  45°  F.     Eelative  humidity,  0.41. 
Temperature  of  radiation  cylinder  =  154°.0  C. 

Mean  temperature  of  radiation  cylinder  (series  4)  =  152°.0  C. 
"  «  "  excess  (series  4)  =  126°.8  C. 

s 

Mean  dew-point,  44°  F.  =  6°.7  C.,  or  pressure  of  aqueous  vapor  =  7.31  mm.,  corresponding  to 
7.55  grams  per  cubic  meter  of  air,  and  to  an  equivalent  depth  of  liquid  water  of  0.000  284  cm. 
in  the  absorbent  layer  of  air. 

Pressure  of  carbon  dioxide,  85  lain. 


58 

TABLE  36. 

(Series  5.) 


Position  of  disk. 

In. 

Out.                  In. 

Depth  of  gas  (feet). 

0.35 

2.0 

0.35 

die. 

99.0 

109.6 

100.2 

99.6 

+10.0 

103.3 

112.9 

101.9 

102.6 

+10.  3 

101  9 

114.0 

103.9 

102.  9       +11.  1 

97.2 

108.4 

97.0 

97.1 

+11.3 

100.2 

108.5 

99.6 

99.9 

+  8.6 

100.0 

111.4 

101.8 

100.9 

+10.5 

101.8 

112.2 

104.4 

103.1 

+  9.1 

99.0 

109.8 

100.2 

99.6 

+10.2 

100.2 

109.2 

101.3 

100.8 

+  8.4 

100.5 

111.1 

103.2 

101.9 

+  9.2 

Differential  radiation  fordepth  (1.65ft.). 

+  9.87 

At  12h  19'",  dry  bulb  =  69°.l  F.  =  20°.6  C. 
wet  bulb  =  58°.6  F.  =  14°.8  C. 
Difference  =  10.5  +  5.3  (correction)  =  15°.8  F. 
Dew  point,  38°  F.     Relative  humidity,  0.32. 
Temperature  of  radiation  cylinder  =  163°.S  0. 

Mean  temperature  of  radiation  cylinder  (series  5)  =  158°.9  C. 
"  "  "   excess  (series  5)  =  133°.4  C. 

Mean  dew-point,  41°.5  F.  =  5°.3  C.,  or  pressure  of  aqueous  vapor  =  6.64  mm.,  corresponding  to 
6.90  grains  per  cubic  meter  of  air,  and  to  an  equivalent  depth  of  liquid  water  of  0.000  259  cm 
in  the  absorbent  layer  of  air. 

Pressure  of  carbon  dioxide  =91  mm. 

Mean  pressure  of  car.bon  dioxide  (series  5)  =  88  mm. 

TABLE  37. 

(Series  6.) 


Position  of  disk. 

In. 

Out. 

In. 

Depth  qf  gas  (feet)  . 

0.35 

5.0 

0.35 

dir. 

103.0 

113.0 

99.3 

101.2 

+11.8 

99.3 

112.  3 

99.3 

99.3 

+13.0 

99.3 

111.0 

97.  3             98.  3 

+12.7 

97.3 

111.2 

94.9 

96.1 

+15.1 

94.9 

108.2 

95.0 

95.0 

+13.2 

95.0 

107.6 

94.0 

94.5 

+13.1 

94.0 

110.0 

94.1 

94.1 

+15.9 

94.1 

108.9 

92.5 

93.3 

+15.6 

92.5" 

108.8 

93.0 

92.8 

+16.0 

93.0 

107.2 

92.0 

92.5 

+14.7 

Differential  radiation  for  depth  (4.65  ft). 

+14.11 

59 

At  12h  26m,  dry  bulb  =  69°.8  F.  =  21°.0  C. 

wet  bulb  =  60°.2  F.  =  15°. 7  C. 
Difference  =  9.6  +  4.8  (correction)  =  14°.4  F. 
Dew-point,  43°  F.     Kelative  humidity,  0.38. 
Temperature  of  radiation  cylinder  =  164°.S  C. 

Mean  temperature  of  radiation  cylinder  (series  6)  =  164°.3  C. 

"  "   excess  (series  6)  =  138°.5  C. 

Mean  dew-point  40°.o  F.  =  4°. 7  C.,  or  pressure  of  aqueous  vapor  =  (3.37  mm.,  corresponding  to 
6.63  grams  per  cubic  meter  of  air,  and  to  an  equivalent  depth  of  liquid  water  of  0.000  249  cm. 
in  the  absorbent  layer  of  air. 

Pressure  of  carbon  dioxide  =  96  mm. 

Mean  pressure  of  carbon  dioxide  (series  6)  =  93.5  mm. 

TABLE  38. — Summary. 


Series. 

Air  layer. 

Carbon  dioxide  in  radiation  cylinder. 

Pressure. 

Water 

cm.  x  10  —  • 

Tempera- 
ture. 

Excess. 

Radiation. 
Pressure.                                                              Ratio 

64.65ft. 

84.65  ~-S  1.65 
51.»>5  ft. 

mm. 

c 

6 

mm.                div. 

dii: 

1  !             734 

227 

123.9 

100.9 

734                  8.  29 

, 

2 

734 

234 

138.1 

114.5 

734 

74a           10-08 

7.42 

3 

734 

244 

145.0 

120.  9 

734               11.87 

=  1.358 

4 

734 

284 

152.0 

126.8 

85               12.  71 

5 

734 

259 

158.  9 

133.4 

88 

13.41 

9.87 

6 

734 

249 

164.3 

138.5 

93.5           14.11 

=  1.359 

As  in  the  case  of  air,  there  is  scarcely  any  difference  in  the  radiation  which  can  be  attributed 
to  change  of  pressure.  The  change  of  radiation  with  the  depth  is  also  unaffected  by  pressure. 

When  the  depth  is  increased  in  the  ratio  ^-^  =  2.818,  the  differential  deflection  is  only  increased 

10.2 
in  the  ratio  1 : 1.359.     Table  31  gives  for  the  same  depths  the  ratio  of  deflections  ->-«-  =  1.342, 

and  the  results  of  Table  31  for  the  2d  and  oth  feet  are  confirmed  by  the  more  elaborate  measures 
of  Table  38. 

Professor  Paschen  ("Emission  erhitzer  Gase.7'  Wied.  Ann.,  Bd.  50,  Taf.  9,  fig.  9,  1893)  gives 
a  series  of  spectral  energy-curves  for  the  principal  maximum  of  carbon  dioxide  at  temperatures 
110°,  158°,  330°,  622°,  710°,  and  973°  C.,  the  radiation  proceeding  from  a  layer  of  the  heated  gas 
about  3  mm.  deep.  At  the  lowest  temperature,  which  is  a  little  below  the  highest  in  my  observa- 
tions, the  deflections  are  very  small,  and  the  spectral  energy-curve  is  very  flat,  but  is  still  shown 
as  a  distinctly  limited  emission-band  whose  extreme  wave-lengths  do  not  differ  by  more  than  a 
fraction  of  a  micron.  Measuring  the  areas  of  the  first  four  curves  of  Paschen's  figure,  the  relative 
radiations  are  found  to  be — 

Temperature  110°        158°        330°        622° 

Eadiatiou*  75          227       1,630      4,905 

Drawing  a  curve  through  these  values,  and  also  (anticipating  a  little)  one  to  represent  my 
final  measures  of  the  total  apparent  radiant  emission,  the  depths  of  radiant  gas  being  3  mm.  and 


Measured  in  arbitrary  units. 


60 


1,418  mm.,  the  following  approximate  relative  radiations  for  moderate  temperature-excesses  have 
been  read  from  the  curves  : 

TABLE  30. 


Depth.             t=2(P 

«=40° 

<=60° 

#=80° 

«=100:             «=12(P 

cm. 

0.3                       1 

4 

12 

30 

59 

100 

141.8                   2 

7 

17 

36 

65 

100 

The  rate  of  increase  of  radiation  with  that  of  temperature  is  greater  for  a  3-inm.  layer  than 
for  one  of  1,418  mm.,  because  the  absorption  in  the  mass  of  great  depth  partly  neutralizes  its  own 
radiation.  This  is  proved  by  the  preceding  experiments,  which  have  demonstrated  that  a  5-foot 
layer  of  carbon  dioxide  radiates  but  little  more  than  a  2-foot  layer,  and  no  more  than  a  3-foot  layer. 
The  rate  of  increase  of  radiation  with  temperature  for  a  5-foot  layer  of  air  does  not  differ  much 
from  the  corresponding  rate  for  carbon  dioxide  at  these  low  temperatures,  and  the  absolute  radia- 
tions also  are  not  very  different;  Out,  unlike  carbon  dioxide,  the  air  radiates  in  proportion  to  the 
depth.  It  may  be  that  this  is  because  the  measured  radiation  of  air  in  my  final  experiments  has 
been  to  a  considerable  extent  that  of  its  oxygen,  nitrogen,  or  argon,  and  not  merely  that  of  the  more 
highly  absorbent  and  at  high  temperatures  more  powerfully  radiant  carbon  dioxide  or  water- vapor. 
Since,  at  high  temperatures  and  in  thin  layers,  the  radiative  power  of  these  strong  absorbents  is 
immensely  greater  than  that  of  air,  it  follows  that  the  rate  of  radiant  increase  with  the  depth  for 
air  at  higher  temperatures  must  be  very  much  slower  than  for  carbon  dioxide,  and  that  at  partic- 
ular depths  and  temperatures,  which  have  been  reached  in  the  present  research,  the  total  radia- 
tions of  these  substances  are  more  nearly  equal.  It  is  not  possible,  however,  that  equable  increase 
of  air  radiation  with  depth  can  continue  indefinitely,  since  the  heat  lost  by  layers  of  such  dimen- 
sions as  we  have  in  the  atmosphere,  and  imparted  by  radiation  from  the  atmosphere  to  the  earth, 
would  have  to  be  much  greater,  in  that  case,  than  it  actually  is. 

The  differential  deflections  in  Tables  30  and  31  may  best  be  compared  by  stating  them  as 
percentages  of  the  deflection  with  disk  at  4  feet. 

TABLE  40. 


Position  of 
disk. 

Depth  of 
gas. 

Air  at 
185°.5  and 
723  mm. 

C02  at              Increase  per  foot. 
19R3  H  nrin 

766  nun.              Air. 

C02. 

Feet. 
0.35 
1.0 
2.0 
3.0 
4.0 
5.0 

cm. 
0 
19.8 
50.3 
80.8 
111.3 
141.8 

0 
18.4 
48.5 
73.6 
100.0 
98.2 

o     

33.3            28.3 
72.  0  f          30.  1 
98.  7            25.  1 
100.  0             26.  4 
97  1        

51.2 
38.7 
26.7 
1.3 

The  slight  decrease  in  the  differential  deflection  at  the  fifth  foot,  as  compared  with  that  at 
the  third  or  fourth  foot  in  the  experiments  with  carbon  dioxide,  is  possibly  due  to  the  chilling  of 
the  radiating  disk  in  the  extreme  end  position,  or  to  absorption  of  disk  radiation  by  CO2,  a  point 
which  will  be  examined  farther  on;  but  the  change  in  the  air  series  at  the  fifth  foot  is  presumably 
to  be  attributed  to  a  different  cause.  The  observations  of  Table  30  were  the  first  made  with  appa- 
ratus C.  Intermediate  positions  were  reached  by  stopping  the  rod  which  carries  the  disk  at 
successive  marks,  but  the  end  reading  was  secured  by  pulling  out  the  disk  until  its  clamp  was  felt 
or  heard  to  strike  against  the  end-plate.  The  supports  of  the  cylinder  were  not  stiff  enough  to 
resist  the  shock,  and  the  entire  mass  of  iron  moved  to  and  fro  though  a  sufficient  range  to  produce 
a  deflection  of  a  few  divisions  on  the  galvanometer  by  magnetic  influence.  Suspecting  such  an 
effect,  which  was,  however,  irregular,  and  one  for  which  no  correction  can  be  applied,  I  had  the 
supports  stiffened  by  braces,  and  the  remedy  proved  effectual.  The  error  only  affects  the  readings 


61 


on  the  fifth  foot  in  Table  30,  and  these  have  been  rejected.  Observations  made  after  the  insertion 
of  the  braces,  and  with  a  cold  cylinder,  to  see  if  any  magnetic  effect  was  exerted  by  the  motion 
of  the  steel  rod,  gave  a  deflection  of  —  0.29  div.  for  the  outward  motion  of  4.65  feet.  As  this  is 
included  in  possible  errors  of  observation,  no  correction  is  applied  for  magnetic  influence. 

The  relative  increments  of  radiation,  given  in  the  last  column  of  Table  40,  demonstrate  that  a 
layer  of  carbon  dioxide,  3  feet  deep,  is  sufficient  to  extinguish  by  its  absorption  practically  all  the 
radiation  of  the  peculiar  quality  emitted  by  this  gas;  and  thus  that  no  further  increase  in  the 
depth  of  the  radiating  layer  is  of  avail  for  adding  to  the  emission  of  the  only  rays  which  this 
substance  is  capable  of  sending  forth.  If  this  is  a  general  law,  the  brilliancy  of  a  glowing  gaseous 
mass  (a  solar  prominence,  for  instance)  depends,  after  a  certain  depth  has  been  exceeded,  entirely 
upon  the  temperature,  but  not  on  the  dimensions  of  the  layer;  and  the  cooling  of  a  gaseous  mass 
of  great  depth  depends  on  the  radiation  of  a  comparatively  shallow  layer  whose  locus  travels 
inward.  It  might  be  inferred  from  the  preceding  experiments  that  layers  of  air  and  of  carbon 
dioxide,  1  foot  deep,  and  at  atmospheric  pressure,  radiate  equally  near  the  temperature  of  boiling 
water  to  an  iuclosure  near  the  freezing  point;  but  these  results  require  the  application  of  further 
corrections  before  the  final  quantitative  values  can  be  stated. 

RADIATION    FROM    MULTIPLE    FLAMES. 

In  order  to  examine  the  effect  of  increasing  depth  on  the  radiation  of  a  gas  at  high  temper- 
ature, a  series  of  five  Bunsen  burners,  with  apertures  2.5  by  0.2  inches,  giving  flat  flames,  were 
arranged  so  that  the  flames  were  presented  broadside  to  the  line  of  sight.  Only  so  much  of  the 


flame  as  could  be  seen  through  the  narrow  aperture  of  the  multiple  tin-plate  screen  was  permitted 
to  radiate  to  the  bolometer.  The  most  distant  flame  was  2  feet  from  the  bolometer;  the  nearest. 
1A  feet.  Exposures  were  made  by  withdrawing  a  blackened  copper  screen  containing  cold  water. 
The  shape  of  the  flame  is  shown,  full  size,  in  fig.  8. 


62 

November  15,  1895. 

Temperature  of  room,  14°.8  C.  Dew-point  7°.8  C.,  corresponding  to  a  pressure  of  aqueous 
vapor  of  7.88  mm.,  or  8.11  grains  per  cubic  meter,  and  to  an  equivalent  liquid  depth  of  0.000  371  cm. 
in  the  distance  to  the  nearest  flame,  and  0.000  494  cm.  in  the  path  to  the  most  distant  flame. 

Battery  galvanometer,  100  div.' 

Shunt  =  0.1451.     Multiplier  =  6.89.     Temperature  of  cold  screen,  10°  to  18°  C. 

TABLE  41. 


X  umber  of  flames. 

B 

4 

3 

2 

,/  most  \ 
\  distant/ 

1  (nearest) 

Depth  of  flaine. 

3.0  cm. 

2.4  cm. 

1.8  cm. 

1.2  cm. 

O.Ccm. 

0.6  cm. 

244.5 

217.5 

175.5 

128.  5 

69 

74 

245 

218 

176 

129 

70.5 

72 

250.5 

219 

176 

129.5 

66.5 

73 

252 

221.  5 

174.5 

128.5 

69 

73 

Deflections 

245.5 

220.5 

177 

130 

70 

73.5 

(Shunted  galvanometer) 

249 

216 

177 

125 

69.5 

75.5 

251.5 

218 

.      174.5 

129.5 

66.5 

77.5 

250.5 

220 

173 

130.5 

71 

73 

252.5 

214 

172.5 

126 

69 

72 

250 

220.5 

177 

130 

71.5 

72.5 

Mean  (shunted) 

249.1 

218.  5 

175.3 

128.7 

69.3 

73.6 

"      (unshunted) 

1723 

1506 

1208 

887 

478 

507 

Change  per  0.6  cm. 

217 

298 

321 

395 

4' 

)3 

The  deflection  on  the  most  distant  single  flame  is  94.2  per  cent,  of  that  on  the  nearest  one,  a 
diminution  which  is  probably  due  to  the  greater  amount  of  water- vapor  traversed  by  the  rays  from 
the  flame  at  the  greatest  distance,  the  radiant  emission  from  the  flame  being  largely  that  of  very 
hot  steam,  and  one  especially  depleted  of  its  peculiar  rays  by  even  a  thin  layer  of  its  own 
substance. 

The  addition  of  successive  flames,  each  new  one  radiating  through  all  the  previous  ones,  gives 
progressively  diminishing  increments  of  radiation,  as  shown  in  the  last  line  of  Table  41.  The  aver- 
age depth  of  each  flame  was  6  mm.,  and  the  indication  is  that  there  will  be  very  little  increase  of 
radiation  for  addition  of  flame-depth  beyond  20  cm.  For  carbon  dioxide,  the  depth  of  the  efficient 
radiant  layer  is  not  over  90  cm,  For  air,  the  efficient  depth  must  be  many  meters. 

CONTINUATION   OF   MEASURES   MADE    WITH    THE    RADIATION   CYLINDER. 

The  next  four  series  of  measures  with  the  radiation  cylinder  have  been  made  with  a  continu- 
ously rising  temperature.  Hence,  according  to  the  general  theory  of  the  apparatus,  the  recorded 
thermometer  readings  are  lower  than  the  true  mean  temperatures  of  the  air  within  the  cylinder, 
by  amounts  which  can  perhaps  be  estimated  later;  but  since  all  of  these  series  have  been  taken 
on  a  common  plan,  and  the  rapidity  of  heating  has  been  nearly  the  same,  the  results  are 
comparable. 

The  curves  of  heating  are  given  in  fig.  9,  abscissa?  being  intervals  from  the  commencement  of 
heating  and  ordinates  being  recorded  cylinder  temperatures. 

The  rate  of  heating  is  a  trifle  slower  for  rarified  air.  Otherwise,  the  heating  curves  are 
similar.  The  throw  of  the  disk  was  to  its  full  extent  in  every  case,  the  radiant  depth  being 
141.8  cm.  Deflections  were  observed  in  groups  of  five  every  six  minutes.  Only  the  mean 
readings  are  given  here. 

February  9,  1893. 


Cylinder  containing  air  at  normal  pressure,  737  mm.,  and  nearly  dry,  but  not  purified  from 
carbon  dioxide. 


63 


/fa*  Cent. 


/oo  -win. 


?ig.  9 


Temperature  of  room,  at  31'  Om,  ll°.l  C.;  at  3h  30m,  12°.2;  at  4h  Om,  13°.3;  at  4h  30™,  14°.4; 
at  5h  Om,  15°.5. 

Mean  dew-point,  4°.4  C.,  corresponding-  to  a  pressure  of  aqueous  vapor  of  6.24  mm.  or  6.50 
grams  per  cubic  meter,  and  to  an  equivalent  liquid  depth  of  0.000  244  cm.  in  the  absorbent  layer. 

Lamps  lighted  at  3h  20m.    Burner  cocks  set  at  35  div. 

The  results  are  platted  in  fig.  10  («). 

Abscissa1  =  temperature-excesses  (uncorrected). 

Ordiuates  =  deflections. 

TABLE  42. 


Cylinder  temperature. 

Bolometer 

Observa- 
tion No. 

Time. 

Mean  tem- 
perature. 

tempera- 
ture. 

Excess. 

Deflection. 

Pressure. 

Before. 

After. 

, 

h.      in. 

o 

o                          o 

o 

0 

div. 

mm. 

1 

3        8 

9.3 

9.3 

16.4 

—  7.  1 

0.  £5 

TW 

2 

3    37 

43.9 

53.2 

48.6 

17.5 

+31.1 

+  8'.50 

1  Vl 

3 

3    43 

53.2 

63.3 

58.3 

17.7 

40.6 

+  9.21 

4 

3    49 

63.3 

72.1 

67.7 

17.9 

49.8 

+11.  88 

5 

3    55 

72.1 

81.4 

76.8 

18.1 

58.7 

+11.  05 

6 

4       1 

81.4 

89.9 

85.7 

18.3 

67.4 

+12.  78 

7 

4      7 

89.9 

98.0 

94.0 

18.6 

75.4 

+12.  33 

8 

4     13 

98.0 

104.4 

101.2 

18.8 

82.4 

+14.  70 

9 

4    19 

104.4 

114.2 

109.3 

19.0 

90.3 

+15.  87 

10 

4    25 

114.2 

122.  1 

118.2 

19.2 

99.0 

+16.  06 

11 

4    31 

122.1 

130.  0 

126.1 

19.  4           106.  7 

+19.  29 

12 

4     37 

130.0 

137.2 

133.6 

19.  7           113.  9 

+21.  66 

13 

4    43 

137.2 

144.0 

140.6 

19.  9           120.  7 

+22.64 

14           4     49 

144.0 

150.  3           147.  2 

1 

20.1 

127.1 

+22.  48 

64 

February  10,  1893. 

Cylinder  containing  partially  dried  air  at  low  pressure. 
Temperature  of  room,  13°.8  to  14°.S  C. 

Mean  dew-point,  6°.7  C.,  corresponding  to  a  pressure  of  aqueous  vapor  of  7.31  mm.,  or  7.56 
grams  per  cubic  meter,  and  to  an  equivalent  liquid  depth  of  0.000  284  cm.  in  the  absorbent  layer. 
Lamps  lighted  at  4h  Om.    Burner-cocks  set  at  35  div. 

TABLE  43. 


Observa- 
tion No. 

Time. 

Cylinder  temperature. 

Mean 
tempera- 
ture. 

Bolometer 
temper- 
ature. 

Excess. 

Deflection. 

Pressure. 

Before. 

After. 

h.     in. 

o 

o 

o 

0 

o 

div. 

mm. 

1 

3    51 

13.6 

13.7 

13.7 

18.8 

—  5.1 

+  0.26 

58.5 

2 

4    14 

28.0 

37.1 

32.6 

19.0 

+13.6 

+  3.91 

56.7 

3 

4    20 

37.1 

48.2 

42.7 

19.1 

23.6 

+  6.73 

60.0 

4 

4    26 

48.2 

58.2 

53.2 

19.2 

34.0 

+  8.16 

64.3 

5 

4    32             58.  2 

67.6 

62.9 

19.2 

43.7 

+  8.38 

68.5 

6 

4    38             67.6 

75.7 

71.7 

19.3 

52.4 

-f  11.  69 

72.3 

7 

4    44 

75.7 

84.0 

79.9 

19.3 

60.6 

+11.  09 

76.8 

8 

4    50             84.0 

93.0 

88.5 

19.4 

69.1 

+12.  26 

81.8 

9 

4    56             93.0 

102.2 

97.6 

19.5 

78.1 

+14.  78 

86.5 

10 

5      2           102.  2 

109.7 

106.0 

19.5 

86.5 

+13.  99 

91.5 

11 

5      8 

109.7 

118.1 

113.9 

19.6 

94.3 

+15.  60 

96.5 

12 

5    14          118.  1 

125.  0 

121.6 

19.6 

102.0 

+17.  22         101.  8 

13 

5    20  i        125.  0 

131.6 

128.3 

19.7 

108.6 

+21.  43         106.  3 

14 

5    26 

131.6 

137.9 

134.8 

19.8 

115.0 

+22.  07         110.  8 

15 

5    32 

137.9 

144.2 

141.1 

19.8 

121.3 

+23.  39 

116.8 

The  results  are  plotted  in  Fig.  10  (6).  The  cold  cylinder  leaked  at  the  rate  of  5  mm.  in  15  min. 
at  the  lower  pressures.  Computing  the  proportional  leakage  for  three  intervals  in  the  above  series, 
and  comparing  the  observed  pressures,  corrected  for  the  expansion  of  air  by  heat,  we  have : 

mm. 

4h  14m  to  4h  44m,  change  of  pressure,  56.7  to  76.8 

By  thermal  change,  56.7  X  [1  +  (60.6—13.6)  X  .00367]  =66.5 


Observed  leakage, 

Leakage,  computed  for  30  min.  interval, 

Residual, 


10.3 
10.0 

+  0.3 


4h  44"'  to  5h  8m,  change  of  pressure,  76.8  to  96.5 

By  thermal  change,  76.8  X[l  +  (94.3  —  60.6)  x  .00367]  =  86.3 

Observed  leakage,  10.2 

Leakage,  computed  for  24  min.  interval,  8.0 

Residual,  +2.2 

5h  8m  to  5h  32'",  change  of  pressure,  96.5  to  116.8 

By  thermal  change,  96.5  X[l  +(121.  3  —  94.3)  X  .00367]=106.0 


Observed  leakage, 

Leakage,  computed  for  24  min.  interval, 

Residual, 


10.8 
8.0 

+2.8 


The  excess  of  observed  pressure  over  computed  at  the  higher  temperatures  is  probably 
to  be  attributed  to  the  real  mean  temperature  being  higher  than  that  assumed  from  thermometer 
readings  in  heating,  as  explained  in  the  general  theory  of  the  apparatus;  but  it  is  possible  that 
the  leaks  may  have  increased  in  the  course  of  the  process  of  heating.  Leaks  in  the  luting  had 
been  started  by  the  previous  day's  heating  and  the  joints  had  to  be  tightened  at  the  beginning  of 
the  observations  of  February  10.  Another  possible  cause  of  the  discrepancy  is  that  some  vapor 
may  have  been  evolved  by  the  heat  at  the  highest  temperatures;  but  in  this  case  some  special 
fluctuation  of  the  readings  of  the  galvanometer  might  be  anticipated,  and  of  this  there  is  no  sign. 


65 

February  24,  1894. 

Cylinder  filled  with  dry  carboii  dioxide  at  atmospheric  pressure,  748  mm. 
Temperature  of  room,  12°.8  C.  at  2h  10"',  to  15°.l  C.  at  3h  47™. 

Dew-point,  1°.4  C.,  corresponding  to  a  pressure  of  aqueous  vapor  of  5.05  mm.,  or  5.32  grams 
per  cubic  meter,  and  0.000  190  cm.  of  liquid  water  in  the  absorbent  air  layer. 
Lamps  lighted  at  2h  19ra.     Cocks  35  div. 

TABLE  44. 


Cylinder  temperature. 

Mean          Bolometer 

Observa- 
tion No. 

Time. 

tempera-        tempera- 
ture,              ture. 

Excess. 

Deflection.     ,    Pressure. 

Before. 

After.     . 

h.     m. 

o 

o 

o                        o 

o 

div. 

mm. 

1 

2    26 

39.8 

52.2 

46.  0             18.  2 

27.8 

+  3.20 

748 

2 

2    32 

52.2 

63.0 

57.  6  !          18.  4 

39.2 

+  4.78 

3 

2    38 

63.0 

75.3 

69.2 

18.5 

50.7 

+  4.51 

4 

2    44 

75.3 

85.8 

80.6 

18.7 

61.9 

+  7.63 

5 

2    50 

85.  8            94.  8 

90.3 

18.8 

71.5 

+  8.53 

6 

2    56 

94.  8           104.  8 

99.8 

19.0 

80.8 

+10.  73 

7 

3      2 

104.8 

111.5 

108.2 

19.1 

89.1 

+  8.10 

8 

3      8 

111.5 

122.8 

117.2 

19.3 

97.9 

+10.  80 

9 

3    14 

122.8 

130.8 

126.8 

19.4 

107.4 

+12.  92 

10 

3    20 

130.8 

136.8 

133.8 

19.6 

114.2 

+13.  49 

11 

3    26 

136.8 

144.1 

140.5 

19.7 

120.8 

+13.  45 

12 

3    32 

144.1 

150.6 

147.4 

19.9 

127.5 

+15.  80 

The  results  are  platted  in  fig.  10  (c). 


June  27, 1894. 


Cylinder  containing  dry  carbon  dioxide  at  atmospheric  pressure,  730  mm.  (at  0°  C.). 

Temperature  of  room,  29°.4  C.,  with  a  rise  of  one-half  degree  per  hour. 

Dew-point,  15°.0  C.,  corresponding  to  a  pressure  of  aqueous  vapor  of  12.67  mm.,  or  12.71 
grams  per  cubic  meter,  and  to  an  equivalent  liquid  depth  of  0.000  478  cm.  in  the  absorbent  layer 
of  air. 

Lamps  lighted  at  3h  32m.     Burner  cocks  at  40  div. 

TABLE  45. 


Observa- 
tion If  0. 

Time. 

Cylinder  temperature. 

Mean  tem- 
perature. 

Bolometer 
tempera- 

Excess. 

Deflection. 

Pressure. 

Before.            After. 

ture. 

h.    m. 

o                        o 

o 

o 

o 

div.                  mm. 

1 

3    51 

61.6 

70.9 

66.3 

34.2 

32.1 

+  5.59 

730 

2 

3    57 

70.9 

81.2 

76.1 

34.2 

41.9 

+  6.64 

3 

4      3 

81.2 

91.2 

86.2 

34.3 

51.9 

+  6.34 

4 

4      9 

91.2 

101.2 

96.2 

34.3 

61.9 

+  8.16 

5 

4     15 

101.2 

111.0 

106.1 

34.4 

71.7 

+  9.50 

6 

4    21 

111.0 

119.6 

115.3 

34.4 

80.9 

+  9.38 

7 

4    27 

119.6 

127.6           123.6 

34.5 

89.1 

+10.  58 

8 

4    33 

127.6 

134.8           131.2 

34.5 

96.7 

+10.  28 

9 

4    39 

134.8           142.9           138.9 

34.6 

104.3 

+  9.72 

10 

4    45 

142.  9           148  6           145.  8 

34.6 

111.2 

+11.  73 

11 

4    51 

148.  6           154.  2           151.  4 

34.7 

116.  7 

+12.  69 

: 

12812— Bull.  G- 


66 


The  results  are  platted  in  fig.  10  (<?).  Fig.  10  (a]  gives  for  air  a  radiation  of  24  div.  at  excess 
130°  C.,  or  0.185  div.  per  degree;  and  fig.  10  (b)  gives  24  div.  for  125°  excess,  or  0.192  div.  per 
degree,  no  appreciable  change  being  produced  by  rarefaction.  Fig.  10  (c)  gives  for  carbon  dioxide 
a  radiation  of  14  div.  for  an  excess  of  120°  C.,  or  0.117  div.  per  degree;  and  fig.  10  (d)  gives  14  div. 


24 
22. 

18 

14 
12. 

10 


L£- 


X 


X 


a 


£ 


4 
2 
0 

rf 


£G 


£ 


& 


10 
g 


o9 


50' 


100 


0 


50' 


100 


10 


for  118°,  or  0.119  div.  per  degree,  both  observations  being  at  atmospheric  pressure.  Reducing 
this  deflection  to  the  galvanometer  constant  of  1893,  it  becomes  0.1254  div.,  and  the  ratio  of  radia- 
tions (141.8  cm.  layer)  is: 

0.1885 
Air :  CO2.     .     .     . 


0.1254 


=  1.50. 


This  ratio  is,  of  course,  only  applicable  to  the  limited  range  of  depth  and  temperature  from 
which  it  has  been  obtained.    The  increase  of  water  in  the  absorbent  layer,  in  the  ratio  iqn  =  2.52 

has  not  affected  the  radiation  of  carbon  dioxide.   The  bands  of  these  substances,  in  the  infra-red, 
overlap  to  some  extent,  but  if  composed  of  fine  lines,  they  need  not  interfere. 

GASEOUS  RADIATION   WITH   A   COOLING   CYLINDER-  (LAMPS   EXTINGUISHED). 

The  next  experiments,  conducted  with  a  cooling  cylinder,  should  give  trustworthy  values 
according  to  the  general  theory  of  the  apparatus. 


67 


June  28,  1894. 

Cylinder  filled  with  dry  carbon  dioxide. 

Temperature  of  room,  30°.4  C. ;   of  bolometer,  35°.4. 

Mean  dew-point,  15.°2  C.,  corresponding  to  a  pressure  of  aqueous  vapor  of  12.84  mm.,  or  12.87 
grams  per  cubic  meter,  and  to  a  liquid  depth  of  0.000  484  cm.  in  the  absorbent  layer  of  air. 

The  measures  were  to  be  made  near  normal  pressure,  and  at  points  marked  with  an  asterisk, 
a  little  carbon  dioxide  was  allowed  to  flow  into  the  cylinder  to  restore  the  pressure.  Each  deflec- 
tion in  the  following  table  is  the  mean  of  five.  The  first  reading  in  each  series  corresponds  to  the 
maximum  temperature  and  is  abnormal: 

TABLE  46. 

Series  1. 


Time. 

Cylinder  temperature. 

Mean  tem- 
perature. 

Excess. 

Cooling 
rate  per    |     Deflection, 
minute. 

Pressure 
at  0°  C. 

Before.            After. 

h  .      m. 

000 

o 

div. 

mm. 

2      8 

744 

2    11.5           133.2           132.8           133.0 

97.6 

0.13 

+15.  68 

2     15               132.8           129.9           131.4 

96.0 

0.73 

+12.  44 

2     17 

731 

2    21.3 

126.  7           124.  3 

125.5 

90.1 

1.10 

+  8.71 

*2    23 

718 

2    29 

751 

2    32 

117.0 

112.4 

114.7 

79.3 

0.81 

+  6.32 

2    35 

742 

2    37 

112.4 

109.0 

110.7 

75.3 

0.67 

+  4.65 

2    39 

737 

2    47 

105.1 

103.8 

104.5 

69.1 

0.48 

+  3.86 

2    48 

726 

Series  2. 

h.      m. 

0 

o 

o 

0 

o 

div. 

mm. 

3    43 

741 

3    45.5 

136.2 

134.4 

135.3 

99.9 

0.36 

+14.  51 

3    48 

734 

3    55 

728 

3    56.5 

128.7 

125.0 

126.9 

91.5 

1.23 

+  9.52 

3    58 

715 

3    59.5 

125.0 

119.9 

122.5 

87.1 

1.70 

+  8.21 

*4     1 

706 

4     14 

741 

4     16.  5           113.  0 

109.4 

111.2 

75.8 

0.72 

+  5.66 

4     19 

739 

4    21               109.4 

105.2 

107.3 

71.9 

1.05 

+  4.55 

4    23 

733 

4    25               105.  2 

101.  7           103.  5 

68.1 

0.88 

+  4.09 

4    27 

729 

The  mean  of  the  observed  pressures  in  the  first  series  is  736  mm.;  in  the  second  730  mm.; 
and  the  mean  cooling  rate  is  0°.80  per  minute. 

On  this  date  a  final  series  was  taken  with  carbon  dioxide  as  the  radiant,  to  see  if  any  effect 
could  be  noted  from  varying  the  pressure  while  the  temperature  remained  constant  or  was  cooling 
very  slowly. 

TABLE  47. 


Temperature. 

Excess. 

Cooling  per 
minute. 

Deflection. 

Pressure. 

o                             o 

o 

div. 

mm. 

134.8 

99.4 

0.53 

+10.09 

739 

135.  0                99.  6 

0.00 

+11.  43 

588 

135.4 

100.0 

0.40 

+11.  19 

401 

134.5 

99.1 

0.20 

+12.  74 

208 

133.8 

98.4 

0.08 

+12.  35 

213 

68 

Here  a  slight  increase  of  the  deflection  was  observed  when  the  pressure  diminished. 

The  next  experiments  were  made  with  air  purified  from  both  aqueous  vapor  and  carbon 
dioxide.  The  air  entered  the  apparatus  through  a  series  of  flasks  and  tubes.  First  came  two 
flasks  (1  and  2)  containing  porous  chloride  of  calcium;  then  (3)  a  long  horizontal  tube  filled  with 
crushed  and  chemically  pure  hydrate  of  sodium,  the  stoppers  being  protected  by  asbestos.  Next 
(4)  came  a  flask  filled  with  a  solution  of  sodium  hydrate  in  glycerin,  through  which  the  air  passed 
in  bubbles  whose  rate  of  flow  could  be  regulated  by  the  graduated  stopcock.  After  this  came  (5) 
another  flask  of  porous  chloride  of  calcium,  and  last  (6  and  7)  two  flasks  containing  flocculent  phos- 
phoric anhydride.  (1)  and  (2)  protect  the  sodium  hydrate  from  atmospheric  moisture;  (4)  is  relied 
on  to  absorb  the  last  traces  of  carbon  dioxide.  The  water  coming  from  the  chemical  reaction 

2  NaOH  +  CO2  =  Ka2CO3  +  H2O, 

is  absorbed  by  (5),  (6),  and  (7). 

Finally  a  bowl  of  phosphoric  anhydride  and,  in  the  last  experiment,  pure  sodium  were 
introduced  directly  into  the  radiation  cylinder  to  absorb  the  small  amount  of  impurity  coming 
from  leakage. 

The  leakage  being  proportionally  very  much  greater  at  low  pressures,  after  a  preliminary 
exhaustion  and  filling,  the  pressure  was  kept  about  50  mm.  below  the  normal  for  a  long  time,  the 
outer  air  flowing  slowly  through  the  flasks  and  completing  the  purification  by  successive  dilutions. 

August  15,  1895. 
Pressure,  731  mm.  at  0°  C. 

Temperature  of  room,  31°.3  C.;  of  bolometer,  36°.3. 

Dew-point,  6°.7  C.  Pressure  of  aqueous  vapor,  7.31  mm.,  or  7.56  grams  per  cubic  meter, 
equivalent  to  a  liquid  depth  of  0.000  284  cm.  in  the  absorbent  layer.  Disk  of  blackened  asbestos. 

Temperature  in  (1)  co 
"         "  (2) 
"   (3) 
Deflections : 


f  from  100°. 

0  to  96°.  4. 

Excess  61°. 

9 

"      91  , 

.5  "  89  .3 

"      54  , 

,1 

"      81 

.0  "  79  .0 

"      43 

.7 

•(1) 
div. 

(2) 
div. 

(3) 
div. 

+13.8 
13.9 

'+7.2 
8.4 

+6.6 
4.2 

14.0 

6.1 

4.3 

11.7 

8.3 

4.7 

11.3 

8.  a 

3.1 

Mean  deflections:      +12.94.         +7.66  +4.58 

August  17,  1895. 
Pressure,  728  mm. 

Temperature  of  room,  29°.9  C. ;  of  bolometer,  34°.9. 

Dew-point,  14°.4.    Pressure  of  aqueous  vapor,  12.19  mm.,  or  12.26  grams  per  cubic  meter, 
equivalent  to  a  liquid  depth  of  0.000  461  cm.  in  the  absorbent  layer.     Disk  of  blackened  asbestos. 

Temperature  in  (1)  cooling  from  92°.  0  to  90°.  9.  Excess  56°.  6. 

"          "   (2)        "         "    79  .5  "  77  .2  "      43  .5 

"          "   (3)        "         "    69  .4  "  68  .0  "      33  .8 

"          "   (4)         "          "    60  .0  "  58  .8  "      24  .5 

Deflections:  (1)  (2)  (3)  (4) 

div.  div.  div.  div. 

5.5  3.7  3.0  2.7 
7.2  4.0  3.2  2.9 

6.6  5.8  2.0  3.1 
7.8  3.8  1.3  2.2 
8.0  4.1  1.0  2.5 


Mean  deflections :        +7.  02  +4. 28  +2. 10  +2. 68 

August  21,  1895. 
Pressure,  735  mm. 

Temperature  of  room,  25°  C. ;  of  bolometer,  30°. 

Dew-point,  4°.7  C.    Pressure  of  aqueous  vapor,  6.37  mm.,  or  6.63  grams  per  cubic  meter,  equiv- 
alent to  a  liquid  depth  of  0.000  249  cm.  in  the  absorbent  layer. 


69 

Temperature  in  (1)  cooling  from  105°.  9  to  105°.  0.     Excess  75°.  5 
'  "  (2)       "  "     100  .0  "     96  .7  "      68  .4 


Deflections: 


(3) 
(4) 

«            « 

89  .5  " 
80  .2  •' 

86  .6 

,77  .2 

"      58  .1 

"      48  .7 

(1) 
div. 

(2) 
div. 

(3) 
div. 

(4) 
div. 

6.0 

7.6 

2.6 

1.6 

7.4 

5.  5 

3.0 

1.1 

9.5 

6.4 

2.0 

2.8 

8.9 

5.7 

2.1 

0.7 

9.3 

5.6 

4.6 

0.8 

Mean  deflections :        +8.  22  +6. 16  +2. 86  +1.  40 

August  22,  18V 5. 
Pressure,  738  mm. 

Temperature  of  room,  27°  C. ;  of  bolometer,  32°. 

Dew-point,  7°.8  C.     Pressure  of  aqueous  vapor,  7.88  mm., or  8.11  grams  per  cubic  meter,  equiv- 
alent to  a  liquid  depth  of  0.000  305  cm.  in  the  absorbing  layer. 


Deflections : 


i(l)  constant  at 

71°.  0. 

Excess  39°.  0 

(2)        " 

(i 

71  .0 

"       39  .0 

(3)  cooling 

from  71°. 

0  to  70  .5 

"       38.8 

(4) 

"     70  . 

5  "  69  .4 

"      38  .0 

(5)         « 

"     69  . 

4  "  69  .0 

"      37  .2 

(1) 

(2) 

(3) 

(4) 

(5) 

div. 

div. 

div. 

div. 

div. 

11.6 

6.8 

5.3 

3.0 

2.3 

8.0 

5.4 

4.8 

5.6 

3.9 

7.0 

6.6 

4.2 

3.4 

2.0 

5.0 

6.1 

5.6 

4.4 

3.4 

5.9 

4.1 

3.3 

3.3 

2.4 

Mean  deflections:       '+7.50  +5.80  +4.64  +3.94  +2.80 

The  radiation  cylinder  on  this  occasion  had  been  heated  for  a  long  time  by  the  two  central 
burners. only.  The  horizontal  inequality  of  temperature  produced  by  the  uneven  heating  persisted 
until  the  end  of  this  series.  The  last  reading  is  nearly  normal. 

Finally  the  radiation  cylinder  was  kept  at  a  nearly  constant  temperature — not  far  from 
100°  C.— for  a  week,  the  air  being  in  contact  with  metallic  sodium.  The  following  readings 
were  taken  during  the  interval: 

September  13,  1895. 

Pressure,  733  mm. 

Temperature  of  room,  26°  C.;  of  bolometer,  31°. 

Dew-point,  12°.2  C.  Water-vapor  pressure,  10.57  mm.,  or  10.71  grams  per  cubic  meter. 
Equivalent  liquid  depth  in  absorbing  layer,  0.000  403  cm. 

Temperature,  100°.0  C.  (steady).    Excess,  69°.0. 

Deflections:  7.3,  6.3,  8.0,  7.8,  8.2;  mean,  +  7.52  div. 

September  14,  1895. 
Pressure,  737  mm. 

Temperature  of  room,  23°.5  C.;  of  bolometer,  28°.5. 

Dew-point,   9°.4  C.     Pressure  of  aqueous  vapor,  8.78  mm.,  or  8.98  grams  per  cubic  meter. 
Equivalent  liquid  depth  in  the  absorbent  layer,  0.000  338  cm. 
Temperature,  97°.8  C.  (steady).    Excess,  69°.3. 
Deflections:  7.0,  8.4,  7.7,  7.0,  4.5;  mean,  +  6.92  div. 

September  19,  1895. 
Pressure,  733  mm. 

Temperature  of  room,  28°.8  C. ;  of  bolometer,  33°.8. 

Dew-point,  17°. 8  C.     Pressure  of  aqueous  vapor,  15.14  mm.,  or  15.04  grams  per  cubic  meter. 
Equivalent  liquid  depth  in  the  absorbent  layer,  0.000  566  cm. 
Temperature,  96°.2  C.  (steady).     Excess,  62^.4. 
Deflections:  8.9,  7.1,  7.2,  9.1,  6.8;  mean,  +7.82  div. 


70 


FINAL  CURVES  OF  APPARENT  RADIATION  BY  METHOD  C. 

Eejecting  the  first  members  of  each   series,  because   they  are  vitiated  by  inequalities  of 
temperature,  the  remaining  deflections  with  carbon  dioxide  on  June  28,  1894  (Table  46),  form  a 

16** 


/4 

12 

10 

8 

6 

4 
2 
0 

/B 

16 

/2 

10 
8 
6 

4 
2 


Ttadiat 


.of 


7? 


Aipipa  pent 


141.8 


Oil 


Jlppa 


1W.S 


Dry 


Cm. 


7) 


cm. 


Jli 


ii*. 


tf 


i/oxlde 


\\ 


of 


+ 

'    4 


<|P=4o/ 
=  739 


too°C. 


2  0  8  mm. 


10°     20°     30°     40°     SO0     60°     70 


<to°    too* G. 


single  consistent  series,  representing  the  maximum  apparent  radiation  from  this  gas,  so  far  as 
radiation  depends  upon  depth,  which  deserves  exceptional  weight  (fig.  11).     Passing  a  mean  curve 


71 


through  these  points  and  those  of  Table  47,  and  multiplying  the  ordinates  by  the  ratio  1.5, 
already  obtained  for  air  radiation  from  a  layer  141.8  cm.  deep,  as  compared  with  the  radiation  of 
a  like  layer  of  carbon  dioxide,  and  reducing  to  like  instrumental  conditions,  a  curve  is  obtained  (fig. 
12)  which  represents,  as  well  as  any  which  I  can  devise,  the  considerable  range  in  air  values  which 
have  been  obtained  between  August  15  and  September  19,  1895.  The  curve  falls  between  the 
observations  of  August  17  and  August  21,  passes  between  the  records  of  radiation  at  stationary 
temperature  of  September  13  and  14,  although  considerably  below  the  stationary  point  of  Sep- 
tember 19,  and  is  sufficiently  below  the  obviously  abnormal  curve  of  August  22  to  be  free  from 
the  suspicion  of  being  affected  by  any  remaining  inequality  of  temperature.  The  readings  of 
August  21  are  a  little  too  small,  the  rock-salt  plate  having  a  deposit  of  dust  on  its  surface.  The 
observations  of  August  15  have  not  progressed  far  enough  to  be  entirely  uninfluenced  by 
inequality  of  temperature.  Even  the  deflections  at  stationary  temperature  may  be  a  little  too 
large  on  this  account,  and  the  curve  should  pass  below  them  rather  than  through  them.  In 
plotting  these  variant  air  values  lines  have  been  drawn  through  the  mean  positions,  showing  the 
extreme  range  in  the  deflections  (fig.  12). 

The  observations  of  carbon  dioxide  radiation  were  made  in  1894,  those  of  air  in  1895.  Conse- 
quently the  ordinates  for  the  curve  in  fig.  12,  obtained  by  multiplying  those  of  fig.  11  by  1.5, 
have  been  further  multiplied  by  the  ratio  of  the  galvanometer  constants  in  those  years,  which,  by 

I  OO 

p.  20,  is  -.  ^  =  1.19,  giving  with  the  condition  of  instruments  in  1895  these  values  for  air  radiation: 
<3b8 

Excess:          10°      20°      30°      40°      50°      60°      70°        80°        90°      100° 
Deflection:  0.38    0.86    1.54    2.50    3.78    5.4G     7.60     10.59     14.52    19.64 
Reduced  with  the  galvanometer  constant  of  1894,  the  following  table  is  obtained,  giving  the 
adopted  apparent  radiations  of  a  141.8  cm.  layer  for  every  tenth  degree  of  temperature  excess  from 
0  to  100°,  as  read  from  the  smooth  curves,  the  values  being  expressed  finally  in  absolute  units,  or 
radims  x  (10)~9 

TABLE  48. 


Temperature 
excess. 

10°. 

20=. 

30°. 

40°. 

50°. 

60°. 

70°. 

80°. 

90°. 

100°. 

CO, 
Air 

</i>. 
0.21 
0.32 

</ir. 

0.48 
0.72 

<Uv. 

0.86 
1.29 

div. 
1.40 
2.10 

div. 
2.12 
3.18 

div. 
3.06 
4.59 

div. 
4.26 
6.39 

div. 
5.93 
8.90 

div. 
8.13 
12.20 

div. 
11.00 
16.50 

CO2* 
Air 

9 
14 

21 
32 

38 
57 

61 
92 

93 
139 

134 
201 

187 
280 

260 
390 

356 
534 

482 
723 

*  Radiation  in  ninth-radims. 

The  measured  gaseous  radiations  are  somewhat  too  small,  because  the  gaseous  absorption  of 
disk  radiation  has  been  greater  with  the  disk  out,  thus  diminishing  the  deflection,  and  because 
the  rock-salt  and  the  absorbent  layer  of  air  have  kept  back  a  part  of  the  radiation  of  the  hot  gas. 

I>y  Method  B  (ante,  p.  44),  the  radiation  of  1  meter  of  moist  air  is  about  0.  000  000  104  radim 
at  40°  excess. 

By  Method  C,  the  radiation  of  dry  air,  reduced  to  the  same  depth,  is  0.  000  000  065  radim  at 
40°  excess. 

Both  radiations  have  been  diminished  by  absorption.  In  particular,  the  result  by  Method  C 
requires  an  increase  of  about  one  third  on  account  of  the  absorption  by  the  rock-salt  plate.  The 
hot  moist  air  might  be  expected  to  radiate  more  powerfully  than  dry  air  at  the  same  temperature, 
and  the  remaining  difference  is  probably  attributable  to  this  qualitative  distinction. 

Although  the  affinity  of  rock-salt  for  moisture  made  the  result  of  the  experiment  somewhat 
problematical,  I  decided  to  try  to  measure  the  radiation  of  water-vapor  by  Method  G,  allowing 
steam  to  run  into  the  hot  and  partially  exhausted  cylinder.  I  had  supposed  at  the  time  of  making 
this  experiment  that  the  gradual  introduction  of  steam  into  a  hot  partially  exhausted  vessel  would 
not  be  attended  by  liquid  condensation.  The  result  proved  that  the  flow  of  steam  was  too  rapid, 


72 

and  that  the  cylinder  should  have  been  full  of  air  at  the  start,  the  air-puinps  being  used  merely 
to  keep  the  pressure  from  rising  much  above  normal.  Hirn,  in  1862,  had  found  that  the  sudden 
diminution  of  pressure  in  steam  at  152°  C.  and  5  atmospheres  pressure,  gave  a  cloudy  condensa- 
tion, but  this  result  was  unknown  to  me  until  I  read  it  in  Preston's  Theory  of  Heat,  published 
about  the  time  of  my  observations.  I  regret  that  the  simple  expedient  of  allowing  air  to  remain 
in  the  cylinder  while  the  steam  was  entering  did  not  occur  to  me  until  after  the  apparatus  was 
dismounted. 

EXPERIMENT   ON   THE   RADIATION   OF    STEAM. 

Temperature  of  room,  33°  C. ;  of  bolometer,  38°. 

Dew-point,  3°.l  C. ;  pressure  of  aqueous  vapor  5.70  mm.,  or  5.96  grams  per  cubic  meter.  Equiv- 
alent liquid  in  the  absorbent  layer  =  0.  000  224  cm.  After  exhaustion  to  79  mm.  the  mean  tem- 
perature of  the  radiation  cylinder  was  132°,  cooling  at  the  rate  of  1°.5  per  minute,  and  the  mean 
deflection  from  air,  at  99°  excess,  was  +  13.02  div.  The  heater,  containing  boiling  water,  was 
then  connected  until  the  pressure  reached  731  mm.,  the  temperature  meantime  rising  to  142°,  or 
to  an  excess  of  104°.  A  mean  deflection  of  +  5.20  div.  was  then  obtained,  followed  by  another  of 
+  4.84  div.,  excess  101°.  Within  15  minutes  after  these  readings,  the  pumps  having  been  worked, 
the  pressure  had  diminished  to  126  mm.,  temperature  135°,  excess  97°.  The  mean  deflection  had 
increased  to  -f  25.62  div.,  the  temperature  being  nearly  stationary. 

Undoubtedly,  the  watery  condensation  at  first  precipitated  a  film  of  moisture,  or  dew,  on  the 
rock-salt,  which  diminished  the  deflection  by  its  irregular  scattering  of  the  rays;  but  when  the 
pressure  was  removed,  this  film  evaporated,  and  even  through  the  now  corroded  rock-salt  plate, 
which  transmitted  scarcely  more  than  two-thirds  of  the  radiation,  this  deflection  of  25.6  div.  was 
measured.  I  infer  that  with  a  clear  plate,  something  like  38  div.,  or  about  70  per  cent,  of  the 
radiation  of  lampblack  at  a  like  excess,  might  be  obtained  from  a  layer  of  steam,  at  126  mm. 
pressure,  142  cm.  deep.  Under  these  circumstances,  and  within  the  range  of  my  observations, 
water-vapor  (with  no  allowance  for  absorption  by  the  vapor  in  the  air  of  the  room),  radiates  about 
three  times  as  powerfully  as  air.  In  small  amount,  however,  water-vapor  radiates  much  more 
than  the  simple  proportion  of  the  quantities  would  indicate. 

EXPLANATION   OF   RESULTS  AT   LOW  PRESSURES. 

I  have  alluded  (ante,  p.  54)  to  the  small  difference  between  deflections  at  ordinary  and  at  low 
pressures  as  being  at  first  sight  surprising;  but  the  explanation  is  simple  enough.  According  to 
Duloug  and  Petit  (Ann.  de  Chimie  et  depliys.  (2),  tome  7,  p.  337, 1817),  convection  in  air  at  720  mm. 
pressure  removes  from  a  hot  body  2.548  times  as  much  heat  as  at  90  mm.  pressure;  but  since  the 
mass  of  unit  volume  is  eight  times  as  great  at  the  higher  pressure,  the  air  heated  by  convection 

o 

at  the  lower  pressure,  (1)  if  equal  volumes  are  set  in  motion,  must  get  t>     „  =3.139  times  as  hot; 

or  else,  (2)  if  the  air  gets  no  hotter,  3.139  times  as  large  a  volume  of  low-pressure  air  must  move 
in  the  convection  current  in  the  same  interval  of  time. 

Under  identical  thermal  conditions,  the  radiation  cylinder  being  heated  by  four  large  Bunsen 
burners,  with  stop-cocks  set  at  35  div.,  air,  first  at  737  mm.  and  second  at  83  mm.  pressure,  was 
heated  to  the  same  extent  (80°. C.)  in  one  hour,  with  little  difference  in  the  radiation  from  the 
heated  air  column.  The  final  temperature  of  the  entire  body  of  mixed  air  may  be  nearly  the  same 
in  either  case,  but  the  radiation  through  the  limited  aperture  should  be  greater  in  the  first  condi- 
tion, because  radiation  increases  more  rapidly  than  temperature,  and  the  smaller  volume  of 
superheated  low-pressure  air  should  have  the  greater  radiant  efficiency.  The  true  rate  of  increase 
of  gaseous  radiation  with  rise  of  temperature,  as  will  be  eventually  shown,  is  such  that  if  the 
temperature  is  three  times  as  great,  the  radiation  is  increased  in  something  like  the  ratio  of  eight 
to  one.  Hence  if  the  volume  of  rarefied  air  has  one-eighth  the  mass,  and  is  three  times  as  hot  as 
the  same  volume  of  high-pressure  air,  the  radiation  per  unit  of  mass  (condition  1)  will  be  eight 
times  as  great  for  the  air  of  smaller  density,  or  identical  per  unit  of  volume  for  either  high  or  low 
pressure.  The  actual  rate  of  heating  depends  on  that  of  the  iron  cylinder,  and  not  on  the  thermal 
capacity  of  the  air,  whose  mass  is  relatively  insignificant.  The  result  of  the  measurements  of 


73 

gaseous  radiation  implies  that  the  volume  of  air  set  in  motion  in  the  unit  of  time  by  convection  is 
independent  of  the  pressure,  but  that  the  temperature  of  this  volume  is  such  that  the  radiant 
effect  of  unit  mass  increases  in  inverse  proportion  to  the  mass  of  unit  volume.  The  argument 
also  implies  that,  at  the  same  temperature,  the  radiant  effect  is  proportional  to  the  mass  of  the 
radiating  gas,  and  is  independent  of  the  volume  which  this  mass  may  occupy,  always  with  the 
provision  that  the  mass  is  a  small  one,  or  not  great  enough  for  the  self-absorbent  action  of 
the  gas  on  its  own  radiations  to  produce  any  essential  modification  of  the  radiant  power. 

Since  the  heating  of  the  bottom  of  the  iron  cylinder  by  the  flames  was  far  from  uniform,  it  is 
evideut,  as  has  been  demonstrated  already  in  other  ways,  that  the  measured  radiation  does  not 
proceed  uniformly  from  the  entire  mass  of  air  in  range  with  the  bolometer,  but  from  local 
columns  of  hot  air  rising  over  the  hotter  spots  in  the  iron  and  passing  into  the  field  of  the 
bolometer-aperture  at  a  volumetric  rate,  as  appears  from  the  present  argument,  which  is  the  same 
in  the  rarefied  as  in  the  denser  air.  It  has  been  shown  that  the  disposition,  or  thermal  condition, 
of  the  components  of  the  radiating  mass  at  the  same  mean  temperature,  and  thence  the  combined 
radiation  of  the  whole,  is  different  according  as  the  cylinder  is  heating  or  cooling,  and  that  the 
true  air  radiation  probably  lies  near  the  values  obtained  with  negative  thermal  rates.  It  is  also 
found  that  the  emission  of  gaseous  radiation  increases  at  a  more  rapid  rate  than  the  temperature, 
so  that  if  ordinates  represent  radiation  and  abscissas  temperatures,  the  curve  should  be  concave 
upward.  Nevertheless,  with  rapid  heating  the  observations  are  well  represented  by  a  straight 
line,  evidently  because  the  diminishing  rate  of  heating  at  the  higher  temperatures  gives  less 
powerful  convection.  Small  but  excessively  heated  volumes,  giving  the  larger  part  of  the 
radiation,  then  become  less  predominant,  as  equilibrium  approaches,  and  the  diminution  of  the 
convection-correction  cuts  off  the  more  rapid  rise  of  the  energy-curve  which  would  otherwise 
occur  at  higher  temperature. 

It  is  possible  that  the  apparent  radiation  of  carbon  dioxide,  at  constant  temperature,  increases 
at  low  pressures  (as  indicated  in  Table  47,  p.  67)  by  not  more  than  30  per  cent,  of  the  value  at 
normal  pressures ;  but  the  variation  is  not  beyond  the  limits  of  error  of  the  observations  on  which 
it  rests. 

According  to  Duloug  and  Petit  (loc.  cit.),  the  cooling  power  of  air,  as  far  as  it  depends  on 
pressure,  is  represented  by  the  ratio  ^n<45  -^-jV'4'"',  and  that  of  carbon  dioxide  by  the  ratio 
p»s\-  _^2)i °-517.  Hence  the  influence  of  change  of  pressure  upon  convection  is  greater  for  carbon 
dioxide  than  for  air,  but  this  is  open  to  various  interpretations.  A  part  of  the  removal  of  heat 
by  gaseous  contact  is  due  to  mass  convection,  and  part  to  the  penetrative  power  of  the  flying 
molecules,  as  G.  Johustoue  Stouey  has  demonstrated  (On  the  Penetration  of  Heat  across  Layers 
of  Gas,  Phil.  Mag.  (5),  vol.  4,  p.  424,  Dec.,  1877);  but  in  either  mode  the  effect  finally  depends 
partly  on  the  capacity  of  the  gas  for  heat,  and  this,  for  equal  volumes,  is  greater  for  carbon 

3307 
dioxide  than  for  air  in  the  ratio          =  1.393;  while  in  part  the  magnitude  of  the  effect  is  con- 

— o  i  o 

487 
nected  with  molecular  velocity,  which  is  greater  for  air  in  the  ratio   ^  =  1.227.     The  combined 

O*/  i 

effect  can  only  be  found  by  experiment.  At  normal  pressure  the  cooling  by  carbon  dioxide  is 
0.965  of  that  by  contact  with  air,  but  at  low  pressures  the  relation  is  reversed. 

METHOD  D.— RELATIVE  RADIATION  OF  AIR  AND  STEAM,  AND  OF  CLEAR  AND  SMOKY  AIR. 

In  this  method  the  cylinder  was  provided  with  a  pressure  gage,  recording  in  pounds  per 
square  inch  to  a  pressure  of  15  pounds  above  the  normal.  The  cylinder  then  served  as  a  reservoir 
for  either  compressed  air  or  steam.  On  opening  a  stopcock  the  air,  or  steam,  issued  from  a  hot 
brass  tube,  one-half  inch  in  diameter,  as  a  hot  jet  between  the  bolometer  and  a  blackened  screen 
containing  water  at  the  temperature  of  the  room.  The  bolometer  was  protected  from  air  currents 
by  a  rock-salt  plate.  In  the  first  experiments  partially  dried  air  was  used.  Three  dishes  contain- 
ing flocculeut  phosphoric  anhydride,  were  placed  on  the  floor  of  the  compression  cylinder,  and  air, 
compressed  by  a  pump,  was  forced  into  the  heated  cylinder,  but  was  not  allowed  to  stand  long 
enough  to  become  thoroughly  dried. 

The  objections  to  the  method  are  that  the  amount  of  the  radiating  gas  can  not  be  accurately 


74 

measured,  aud  that  its  temperature,  after  leaving  the  nozzle,  is  lowered  by  mixture  with  cold 
surrounding  air.  For  these  reasons  the  deflections  have  only  a  relative  value.  The  temperature 
of  the  room,  owing  to  the  escape  of  considerable  volumes  of  hot  air  or  steam,  rose  rather  rapidly, 
but  was  kept  within  bounds  by  opening  windows. 

September  28,  1895. 

Temperature  of  room  varying  from  16°.7  C.  to  22°.0. 

Mean  dew  point,  8°.3  C.    Pressure  of  water  vapor,  8.15mm.,  or  8.37  grams  per  cubic  meter. 

Temperature  of  air  blast  on  issuing,  (1)  140°,  (2)  221°. 

Mean  deflections,  (1)  1.94  div.,  (2)  3.45  div. 

September  30,  1895. 

Mean  temperature  of  room,  15°.6  C. 

Mean  dew-point,  6°.l  C.     Pressure  of  aqueous  vapor,  7.02  mm.,  or  7.27  grams  per  cubic  meter. 

After  several  charges  of  steam  had  been  allowed  to  escape  in  order  to  remove  the  air  from 
the  cylinder,  readings  were  begun.  The  deflections  increased  as  the  steam  became  purer.  The 
following  successive  readings  were  taken :  +  4.6,  +  5.8,  +  7.0,  +  8.1,  +  9.8,  +  9.8,  4- 10.3,  -f  11.0, 
+9.5,  +  11.0,  +  11.6,  +  11.0.  The  temperature  having  fallen  slightly  during  the  last  readings, 
the  cylinder  was  left  to  heat  a  little  longer,  and  the  final  measures  were  made. 

Temperature  of  steam  blast  on  issuing,  202°  C. 

Mean  deflection,  +  12.39  div. 

Corresponding  air  deflection,  +  3.07  div. 

Steam  radiation  four  times  as  great  as  that  of  air.  The  undried  air  between  the  bolometer 
aud  the  jet  has  probably  absorbed  more  of  the  aqueous  radiation  than  of  that  from  the  air,  so  that 
the  ratio  is,  if  anything,  too  small. 

The  superheated  steam,  on  issuing,  formed  mist,  and  a  part  of  the  radiation  comes  from  finely 
divided  liquid;  but  the  next  experiment  does  not  indicate  that  these  condensed  particles  can  have 
any  great  effect  on  the  result. 

In  order  to  test  the  possibility  of  appreciable  radiation  from  fine  particles  suspended  in  air, 
two  wide-mouthed  bottles  were  prepared  with  dipping  inlet  and  free  outlet  tubes,  the  first  one- 
fourth  filled  with  strong  ammonia  water,  the  second  containing  about  as  much  hydrochloric  acid. 
Air  from  a  foot  bellows  was  blown  through  the  coupled  flasks,  and  a  dense  column  of  chloride  of 
ammonium  smoke  arose  immediately  in  front  of  the  hot  blast  nozzle.  As  soon  as  the  hot-air  blast 
was  turned  on,  this  cloudy  column  was  sheared  off  and  mingled  with  the  hot  air.  About  one- 
fourth  as  much  air  issued  from  the  smoke  jet  as  from  the  hot  blast,  but  the  latter  can  not  have 
been  cooled  thereby  much  more  than  in  the  ordinary  suction  and  mingling  of  the  surrounding  air. 
The  particles  being  excessively  fine,  and  comparable  in  their  dimensions  with  the  shorter  waves 
of  light,  as  shown  by  the  blueness  of  the  smoke  where  it  was  thinner,  the  microscopic  crystals 
must  have  taken  the  temperature  of  the  air  in  which  they  were  immersed  almost  instantly.  The 
cloud  appeared  fully  as  dense  as  the  mist  from  the  condensed  steam  in  the  previous  experiment. 

October  3,  1895. 

Temperature  of  room,  17°.7  0.  to  18°.8. 

Mean  dew-point,  4°.4  C.    Pressure  of  aqueous  vapor,  6.24  mm.,  or  6.50  grams  per  cubic  meter. 
Temperature  of  hot-air  blast,  200°  C. 

The  range  of  pressure  was  a  little  lower  than  in  the  experiments  of  September  28,  and  the 
deflections  are  therefore  a  little  smaller,  but  all  are  comparable  with  each  other. 


75 
TABLE  49. 


First  series. 

Second  series. 

Third  series. 

Air  3lear. 

Air  clonrtv 
with  XHjCl. 

Air  clear. 

div. 

div. 

div. 

+1.6 

+2.0 

+2.4 

2.7 

1.8 

2.0 

1.7 

2.6 

1.2 

2.3 

1.3 

0.7 

2.4 

1.3 

4.0 

0.7 

2.8 

2.1 

3.9 

2.0 

2.8 

2.0 

1.  1 

1.2 

1.5 

2.5 

1.4 

1.5 

1.5 

1.2 

1.2 

2.1 

2.3 

Means  -j-1.  95 

+1.91 

+1.75 

There  is  no  appreciable  difference  between  the  radiation  of  clear  and  of  smoky  air  in  small 
masses,  but  it  would  not  be  safe  to  generalize,  from  this  experiment,  in  regard  to  radiation  from 
large  masses  of  smoky  air. 

COMPARISON  OF  SOME  OF  THE  PRECEDING  RESULTS  WITH  THOSE  OF  TYNDALL. 

The  experiment  suggested  by  Professor  Abbe  in  its  simplest  form  (Prefatory  note,  pp.  1-2) 
has  been  partly  realized  in  Method  D,  with  the  exception  of  the  unessential  addition  of  a 
background  at  the  temperature  of  melting  ice,  and  it  has  also  been  performed  by  Tyndall 
(Contributions  to  Molecular  Physics  in  the  Domain  of  Radiant  Heat,  p.  42  et  seq.,  American  edition 
of  1873.)  As  a  method  of  heating  an  air  jet,  Professor  Tyndall's  placing  of  a  hot  copper  ball  within 
a  ring  nozzle  may  have  been  efficient,  but  neither  the  temperature  nor  the  mass  of  the  air  can  be 
accurately  measured  in  this  way.  The  results  are  therefore  only  qualitative.  The  deflection  from 
hot  air  being  0°,  that  from  carbon  dioxide  is  given  as  18°  (p.  43  loc.  cit.)',  but  this  does  not  fully 
express  the  facts.  It  is  true  that  when  air  was  turned  on  through  the  nozzle  the  deflection 
did  not  increase,  but  hot  air  was  already  passing  before  the  thermopile  by  simple  convection. 
We  read  further: 

The  radiation  from  air,  it  will  be  remembered,  was  neutralized  by  the  large  Leslie's  cube,  and  hence  0°  attached 
to  it  merely  denotes  that  the  propulsion  of  air  from  the  gas  holder  through  the  Argand  burner  (or  annular  nozzle) 
did  not  augment  the  eft'ect. 

The  18°  from  carbon  dioxide  is  therefore  a  differential  effect,  and  requires  the  original  deflec- 
tion, without  compensating  cube,  for  its  interpretation,  but  this  is -nowhere  stated. 

The  jet  of  heated  gas  in  Tyndall's  experiment  was  of  relatively  small  thickness.  With  a 
deeper  layer  the  relative  position  of  the  two  gases  in  question,  as  radiants,  may  be  more  nearly 
equal,  since,  as  I  have  shown,  air  radiation  from  layers  increasing  up  to  several  feet  in  thickness, 
varies  nearly  as  the  depth,  while  the  radiation  of  carbon  dioxide  soon  reaches  a  maximum. 

Variations  in  the  ratio  of  radiation  with  increasing  depth  are  noteworthy  in  other  gases,  as 
in  Tyndall's  Contributions  (p.  97),  where  a  layer  of  olefiant  gas  (C2H4)  having  a  depth  of  eleven 
units,  radiated  1.62;  and  one  of  air  of  the  same  depth,  containing  one-sixtieth  of  ether-vapor 
(C2H5)2O,  radiated  5.82,  the  radiation  from  unit-depth  of  each  gas  being  taken  as  unity. 

The  figures  quoted  above  for  radiation  of  air  and  carbon  dioxide  are  of  an  indeterminate 
ratio,  but  the  absorption  of  33  inches  of  carbon  dioxide  for  radiation  from  a  copper  plate,  "raised 
to  a  temperature  of  about  270°  C."  (loc.  cit.,  p.  72),  is  stated  (loc.  cit.,  p.  80)  to  be  ninety  times  that  of 
air.  Even  if  the  radiations  of  large  masses  of  air  and  carbon  dioxide  are  equal  at  some  specified 
temperature,  those  of  thin  layers  or  jets  must  nevertheless  be  very  unlike,  the  radiation  from  the 
thin  jet  of  air  being  much  smaller  than  that  from  a  carbon  dioxide  jet.  Other  temperatures  may 
yield  different  radiation-ratios  for  the  two  gases,  while  absorption  varies  at  a  still  different  rate. 
Consequently,  no  safe  inference  as  to  radiation-ratios  can  be  drawn  from  those  for  absorption. 


76 


This  is  shown  by  the  following  observations  by  Pascheu  for  the  principal  band  in  the  spectrum  of 
carbon  dioxide  at  4.25/1  (  Wied.  Ann.,  Bd.  51,  S.  20,  1894): 

TABLE  50. 


Temperature  of 
7  cm.  layer  of  CO2. 

Intensity  of 
radiant  emission. 

Absorption  by 
hot  +  cold  CO2. 

°  C. 

mm.  div. 

Per  cent. 

17 

0 

89 

183 

17.5 

77.5 

290 

60 

68.6 

377 

118.7 

36.7 

480 

261 

19 

The  absorption  is  that  produced  within  the  limits  of  the  band  on  the  spectral  energy-curve  of 
blackened  platinum  at  400°  to  500°  C.  The  small  remaining  absorption  band  at  the  highest  tem- 
perature has  a  wave-length  0.17/<  shorter  than  the  corresponding  emission  band,  and  is  due  to  cold 
carbon  dioxide  in  the  air  of  the  room,  the  radiation  of  the  hot  gas  very  nearly  neutralizing  the 
absorption  by  the  hot  gas  at  480°. 

On  page  95  of  the  Contributions,  Tyudall  gives  the  ratio  of  apparent  radiations  from  carbon 
dioxide  and  air,  dynamically  heated  by  compression,  as  3 : 1,  and  on  page  186  deflections  are  given 
whose  ratio  is  2:1.  But  these  figures  are  not  considered  entirely  trustworthy,  since  the  radiation 
measured  is  supposed  to  be,  to  an  uncertain  extent,  that  of  the  end  plate  and  walls  of  the  contain- 
ing tube,  heated  by  contact  with  the  hot  compressed  gases;  and  any  differences  in  the  observed 
radiation  are  to  be  attributed  partly  to  the  varying  readiness  with  which  heat  is  transferred  by 
conduction  and  convection  from  the  gas  to  the  solid,  and  partly  to  differences  in  the  amounts  of 
heat  produced  by  compression  and  transferred  in  this  manner.  Professor  Tyndall,  in  pointing  out 
some  of  the  defects  of  the  arrangement,  says : 

A  brass  tube  3  feet  long  and  very  slightly  tarnished  within  was  iised  for  dynamic  radiation.  Dry  air  on 
entering  the  tube  produced  a  deflection  of  12°.  The  tube  was  then  polished  within  and  the  experiment  repeated; 
the  action  of  dry  air  was  instantly  reduced  to  7C.5.  The  rock-salt  plate  at  the  end  of  the  tubs  was  then  removed 
and  a  lining  of  black  paper  2  feet  long  was  introduced.  The  tube  was  again  closed,  and  the  experiment  of  allowing 
dry  air  to  enter  it  repeated.  The  deflections  observed  in  three  successive  experiments  were  80°,  81°,  80°  [correspond- 
ing to  a  force  nearly  70  times  as  great  as  the  first].  *  *  A  coating  of  lampblack  within  the  tube  produced  the 
same  effect  as  the  [black]  paper  lining;  common  writing  paper  was  almost  equally  effective.  (Loc.  cit.,p.  187.) 

Now,  the  paper,  being  a  poor  conductor,  must  acquire  on  its  inner  and  radiative  surface,  by 
direct  contact  with  the  dynamically  heated  gas,  a  higher  temperature  than  the  brass,  in  which 
any  gain  of  surface  temperature  is  quickly  distributed  to  deeper  layers  of  metal;  but  the  thin 
coating  of  lampblack,  backed  by  conducting  metal,  is  in  an  intermediate  position  as  a  conductor, 
and  might  be  expected  to  take  on  its  radiating  surface  a  temperature  at  any  rate  lower  than  that 
of  the  paper;  yet  both  blackened  paper  and  blackened  brass  are  said  to  have  behaved  alike. 
Tyndall's  explanation  that  the  deflection  of  7°.5  is  mainly  due  to  radiation  from  brass  to  which 
heat  from  the  compressed  air  has  been  transferred,  can  hardly  be  maintained  without  modification, 
since  blackened  brass  is  not  70  times  as  good  a  radiator  as  bright  brass,  and  no  inconsiderable 
part  of  the  7°.5  may  have  been  true  air  radiation.  I  shall  return  to  this  point  subsequently 
(p.  110)  with  fresh  material  for  a  more  searching  test  of  its  truth. 

The  long  tube  in  Tyndall's  research  was  made  of  polished  metal,  and  the  thermopile  was  pro- 
vided with  its  conical  polished  reflector,  in  order  to  secure  the  advantage  of  larger  galvanometer 
deflections,  through  multiple  reflections  at  large  angles  of  incidence  on  the  inner  walls  of  the  tube 
in  those  experiments  where  an  independent  source  of  radiation  was  situated  at  or  beyond  the 
farther  end  of  the  tube.  When  such  a  tube  is  used  for  the  dynamic  heating  of  a  gas,  a  large  part 
of  the  heat  produced  by  gaseous  compression  is  unquestionably  transferred  to  the  walls  of  the 
tube;  but  since  the  mass  of  the  gas  and  its  thermal  equivalent  are  small,  while  those  of  the  tube 
are  at  least  several  hundred  times  greater,  the  tube  can  not  become  much  heated  unless  the  process 
is  repeated  a  great  many  times.  The  large  deflections  from  lampblack  and  paper  are  possibly 


77 


produced  by  a  special  condensation  and  development  of  heat  in  the  pores  of  these  substances. 
The  argument  on  page  186  of  the  Contributions,  which  makes  a  "residual  deflection  of  6°"  (after 
absorption  by  an  extra  13  inches  of  quiescent  carbon  dioxide)  represent  the  radiation  of  polished 
brass,  does  not  appear  to  be  conclusive,  and,  in  fact,  is  put  forth  rather  as  a  surmise. 

Admitting  the  deflections  to  be  of  genuine  gaseous  origin,  Tyudall's  observations  would  make 
a  3-foot  layer  of  carbon  dioxide  radiate  two  or  three  times  as  much  as  air.  In  my  experiments 
the  air  apparently  radiated  twice  as  strongly  as  the  carbon  dioxide.  In  view  of  the  very  powerful 
radiation  from  water-vapor,  and  of  the  difficulty  with  which  this  substance  is  completely  elimi- 
nated, it  may  be  urged  that  my  samples  of  air  were  not  dry;  but  since  greater  precautions  were 
taken  in  drying  the  air  than  in  drying  the  carbon  dioxide,  the  latter  being  merely  passed  through 
several  flasks  of  porous  calcium  chloride,  while  the  air,  in  some  of  my  experiments,  had  stood  for 
a  week  in  contact  with  phosphoric  anhydride,  I  do  not  think  that  the  larger  radiation,  where  air 
was  used,  can  have  proceeded  from  aqueous  vapor  in  my  samples.  Only  one  of  my  air  series  gave 
deflections  as  small  as  for  carbon  dioxide,  and  this  I  have  had  to  discredit,  owing  to  a  deterioration 
of  the  rock-salt  plate. 

Thus  far  we  meet  only  uncertainty  and  discrepancy,  but  if  the  reader  will  have  patience  all 
of  this  shall  eventually  be  cleared  away. 

It  is  desirable  to  have  a  more  careful  analysis  of  TyndalFs  experiment  than  is  given  in  the 
original  memoir.  Where  the  most  distant  part  of  the  tube  was  set  off  as  a  radiant  chamber  by  a 
rock-salt  partition  the  direct  radiation  of  its  contained  gas  or  walls  was  received  under  a  smaller 
angular  aperture  and  with  proportionally  smaller  effect  than  where  the  partition  was  nearer  to 
the  thermopile;  but  the  concentration  of  the  beam  reflected  from  the  polished  cylindrical  walls  of 
the  tube  was  nearly  the  same  in  either  case.  The  diameter  of  the  tube  is  not  stated.  I  will 
assume  it  to  have  been  2.4  inches,  as  in  another  case,  and  the  distance  of  the  thermopile  from  the 
nearer  end  of  the  tube  to  have  been  0  inches,  and  thus  compute  the  angular  areas  of  the  sections 
on  these  assumptions.  The  lengths  and  deflections  in  the  following  table  are  taken  from  Tyndall's 
Table  XXXV  for  carbon  dioxide,  and  the  radiant  energies  are  deduced  from  the  deflections  by 
the  calibration  of  the  galvanometer.  (Contributions,  p.  57.) 

di  is  the  distance  in  inches  to  the  nearest  section. 
d.2  =  "        "         "        "      "     "   farthest      " 
l  =  dt —  f?i  =the  length  of  the  radiating  column. 
at  =  the  angular  area  of  the  nearest  section. 
az=  "        "  "      "    •'    farthest     " 

TABLE  51. 


l 

2 

3                   4 

5 

6 

dt 

52.6 

40.0 

19.1 

6.0 

6.0 

6.0 

d> 

55.4 

55.4 

55.4 

19.1 

40.0 

52.6 

I 

2.8 

15.4 

36.3 

13.1 

34.0 

46.6 

a\ 

7 

12 

32 

511 

511 

511 

«2 

6 

6 

6 

52 

12 

7 

(a,+fl.;)-2 

6.5 

9 

29 

281.5 

261.5 

259 

Deflection 

1 

3.7 

16.8 

17.5 

23.3 

33.6 

Radiation 

1 

3.7 

17.2 

18.0 

25.7 

48.6 

Between  (4;  and  (5)  there  is  an  increase  of  20.9  inches  in  the  length  of  the  radiating  column, 
and  the  radiation  is  greater  by  7.7  units;  but  with  a  further  addition  of  12.6  inches  to  the  leugth  in 
(6),  the  radiation  gains  22.9  units,  or  three  times  as  much  as  for  the  larger  increment  of  length  in 
(5).  Table  XXXIY,  for  carbon  monoxide,  gives  a  very  different  relation  for  the  same  distances, 
the  increment  of  radiation  in  (5)  being  10.4  units,  and  in  (G)  6.0  units,  numbers  which  are  nearly 
proportional  to  the  gain  in  length.  I  have  no  hesitation  in  saying  that  the  deflection  from  CO2in 
(6)  is  a  mistake.  The  33°.6  is  possibly  a  misprint  for  23°.6,  since,  as  I  have  shown,  there  is  no 
increase  in  the  radiation  of  carbon  dioxide  beyond  the  third  foot. 

The  deflection  in  (1) — Table  51 — is  too  small  for  use;  but  with  a  trifling  addition  to  the  radia- 


78 


tioiis  in  (4)  and  (5),  reducing  them  to  the  lengths  of  (2)  and  '(3),  we  may  make  the  following 
comparison : 

TABLE  52. 


^tin^  column1"  Kadiation  c°2- 

Ratio. 

Mean  angular 
area. 

Ratio. 

Inches. 

36 

15 

17-26 
4-19 

1:1.53 
1:4.75 

29-261 
9-282 

1:9 
1:31 

Ratio  of  ratios, 

1:3.10 

1:3.44 

The  changes  seem  to  be  mainly  due  to  differences  in  the  angular  area,  but  this  influences 
principally  the  radiation  which  comes  directly  to  the  thermopile,  and  the  total  radiation  from  the 
gas  is  made  up  approximately  as  follows: 

Length.  Reflected  radiation.        Direct  radiation.        Total. 

15  inches  }  <2>  °' 5          =   4'  ° 

<(4)  3.5  +(0.5x31)       =19.0     • 

36  inches  p)  "       =17'° 

<(5)  15.9  +    (1.1x9)       -^25.8 

These  radiations  appear  to  be  genuine,  but  there  is  no  conclusive  evidence  that  the  radiation 
of  polished  brass  has  contributed  to  them  appreciably.  The  observations  on  air  are  not  given  in 
detail,  and  we  only  know  from  page  186  that  whereas  the  3  foot  layer  of  CO2  gave  a  deflection  of 
16°.8,  dry  air  gave  8°  or  9°. 

The  temperatures  of  the  gases  are  not  so  easily  found.  In  general,  the  temperature  of  a  gas 
being  the  sum  of  the  kinetic  energies  of  its  molecules,  divided  by  their  number,  may  be  very  differ- 
ently constituted  according  as  the  limits  of  variation  of  molecular  velocity  are  wide  or  narrow. 
Eadiation  and  absorption  within  the  gas  need  also  to  be  considered.  In  the  present  case  the  radi- 
ation has  been  measured  in  the  midst  of  a  complex  series  of  operations,  and  we  do  not  know  even 
approximately  what  proportion  of  the  heab  of  compression  has  been  ceded  to  the  metal.  Professor 
Tyndall  has  attempted  a  thermometric  measurement  of  the  temperature  of  the  dynamically  heated 
gas,  which  may  be  given  for  whatever  it  is  worth.  He  ;'had  the  tube  perforated  and  delicate 
thermometers  screwed  into  it  air-tight.  On  filling  the  tube  the  thermometric  columns  rose,  on 
exhausting  it  they  sank,  the  range  between  the  maximum  and  minimum  amounting  in  the  case  of 
air  to  5°  F."  (loc.  cit.,  p.  45).  If  the  proportion  of  heat  transferred  to  the  walls  is  the  same  in  the 
two  gases,  we  must  conclude  that  at  excesses  of  a  few  degrees  carbon  dioxide  radiates  more  than 
air;  but  the  observation  is  open  to  the  interpretation  that  the  proportion  of  heat  given  to  the 
walls  is  not  the  same  for  either  gas,  and  the  precise  ratio  has  still  to  be  determined.  Some  varia- 
tions in  the  ratio  of  gaseous  radiations  at  different  temperatures  need  not  surprise  us,  since  the 
radiations  are  made  up  of  bands  of  very  different  wave-lengths  with  various  rates  of  increase  by 
change  of  temperature.  Even  solid  bodies  may  have  spectral  energy-curves  of  quite  different 
shape,  as  I  have  shown  in  a  comparison  of  the  spectra  of  the  Welsbach  light  and  of  the  illumi- 
nating gas  flame  of  an  Argand  burner.  ("Further  considerations  in  regard  to  laws  of  radiation." 
Astrophysical  Journal,  vol.  4,  p.  45,  June  1806).  The  relative  radiations  of  particular  wave-lengths 
for  these  lights  vary  nearly  as  1  to  4  in  different  parts  of  the  spectrum,  the  spectral  energy-curves 
crossing  and  recrossing,  and  much  wider  ranges  occur  in  gases  where  each  baud  has  a  law  of  its 
own.  Before  arriving  at  a  more  definite  conclusion  a  further  study  of  the  relation  between 
gaseous  radiation  and  absorption  must  be  made. 

MODIFICATION   OP   ATMOSPHERIC   RADIATION    BY   THE   ABSORPTION    OP    CONSTITUENT 

GASES   AND    VAPORS. 

Having  made  a  preliminary  clearing  of  some  of  the  sources  of  error  incidental  to  the  appara- 
tus, the  method  of  observation,  and  the  properties  of  matter,  we  are  now  prepared  to  take  up  a 
very  important  subject — the  modification  of  radiation  from  gases  or  solids  by  gaseous  absorption. 


79 

Gaseous  radiation  and  absorption  are  so  intricately  interwoven  that  one  can  not  be  explained 
without  also  considering  the  other.  Observations  of  gaseous  absorption  exist  in  great  abundance, 
but  those  on  gaseous  radiation  are  comparatively  few.  It  is  largely  in  consequence  of  this  one- 
sided distribution  of  evidence  that  so  many  questions  in  this  department  remain  open,  and  that 
others  which  have  really  been  settled  for  a  long  time  do  not  obtain  recognition  or  are  reopened  on 
insufficient  grounds. 

The  chief  absorbent  of  the  Earth's  atmosphere  is  water-vapor,  but  its  action  is  complicated  by 
the  relation  between  vapor  and  mist.  Even  considerable  changes  in  atmospheric  aqueous  vapor 
in  warm  weather,  if  unattended  by  misty  condensation,  produce  only  slight  variation  in  the  direct 
rays  of  the  midday  sun,  not,  however,  because  water- vapor  does  not  exercise  a  great  absorption, 
even  on  solar  rays,  but  because  so  much  moisture  is  always  present  in  warm  weather  that  nearly  all 
of  the  rays  absorbable  by  aqueous  vapor  have  been  eliminated,  and  the  remaining  radiation  is 
comparatively  transmissible.  Haze,  however,  of  whatever  description,  whether  formed  of  mineral 
particles,  smoke,  or  finely  divided  liquid  or  solid  water,  acts  at  all  seasons,  and  independently  of 
the  amount  of  the  vapor  of  water  dissolved  in  the  air.  Mist  and  haze  have  little  effect  on  the 
emission  of  radiations  of  long  wave  length  from  air  by  virtue  of  its  own  temperature,  or  on  the 
transmission  of  long  ether- waves  by  the  atmosphere,  but  they  have  great  influence  in  stopping  and 
scattering  those  short  ether- waves  which  are  especially  prominent  in  sunlight. 

Ferrel  says  (Recent  Advances  in  Meteorology,  p.  56,  fl  43, 1886)  <•  the  difference  in  the  intensity 
of  the  solar  rays  at  the  earth's  surface  at  sea  level,  when  the  atmosphere  is  very  clear  and  when  it 
is  somewhat  hazy,  is  small,  and  therefore  the  whole  diminution  of  intensity  in  passing  through  is 
due  mostly  to  the  pure  atmosphere;"  but  this  is  not  correct.  The  direct  rays  of  the  sun  are  much 
impeded  by  haze,  but  are  nevertheless  nearly  as  effectual  in  warming  the  earth's  surface  indirectly, 
because  a  large  part  of  the  rays  scattered  by  the  haze  still  reaches  the  earth  as  sky  radiation, 
which  bears  an  increasingly  large  proportion  to  the  direct  solar  rays  as  haze  grows  denser.  In  a 
general  way,  this  influence  of  the  scattering  of  light  by  fine  particles  is  recognized  by  Ferrel  on 
page  59  of  the  same  work,  but  its  application  to  the  point  noted  on  page  56  escaped  his  attention. 

Other  inconsistencies  occur  in  the  same  connection.  Thus,  on  page  59,  we  read :  "  It  is  thought 
that  pure  dry  air  absorbs  very  little  of  the  sun's  [radiant]  heat  in  its  passage  through  to  the  earth. 
If  so,  the  loss  of  intensity  must  be  caused  mostly,  in  this  case  at  least,  by  the  irregular  reflections  in 
all  directions."  But  at  the  end  of  the  same  paragraph  it  is  said  that  these  reflections  "  depend  very 
much  in  some  way  upon  the  vapor  contained  in  [the  clear  atmosphere]  where  it  exists.  But  as  this 
is  found  mostly  in  the  lower  strata  near  the  earth's  surface,  and  only  in  a  small  measure  in  the 
middle  and  upper  strata  of  the  atmosphere,  its  effect  is  small  in  comparison  with  that  of  the  whole 
depth  of  a  dry  atmosphere."  The  only  idea  which  I  can  derive  from  the  passages  which  I  have 
italicized  is  that  pure,  dry  air  influences  the  sun's  radiation  very  little,  and  mainly  by  irregular 
reflection,  while  water  vapor  is  even  less  effective.  The  last  inference  is  further  emphasized  in 
paragraph  44,  page  56:  "According  to  the  experiments  of  Dr.  Tyudall  on  the  diathermancy  of  a 
small  portion  of  air  contained  in  a  tube,  with  regard  to  heat  radiations  from  terrestrial  sources 
the  diathermancy  of  clear  air  depends  almost  entirely  upon  the  aqueous,  invisible  vapor  in  it,  sev- 
enty times  as  much  heat,  according  to  the  result  of  the  experiments,  being  absorbed  by  it  as  by  the 
dry  air  through  which  the  rays  pass.  This  result,  however,  differs  very  much  from  that  which  had 
been  obtained  by  Magnus  in  experiments  on  the  same  subject,  and  this  gave  rise  to  considerable 
discussion  between  these  physicists,  Magnus  maintaining  that  the  absorption  of  heat  in  Tyndall's 
experiments  was  by  a  film  of  condensed  vapor  on  the  inside  of  the  tube  through  which  the  rays 
passed.  And  this  seems  really  to  have  been  the  case,  according  to  experiments  which  have  since 
been  made  to  verify  the  results."  Nevertheless  the  opinion  is  repeatedly  expressed  elsewhere  (as 
on  page  57  loc.  cit.)  "that  aqueous  vapor  in  some  way  diminishes  the  diathermancy  of  the  atmos- 
phere to  terrestrial  heat  radiation."  The  only  inference  which  I  can  draw  is  that  the  entire  subject 
was  in  a  state  of  hopeless  confusion  in  the  mind  of  one  who  has  elsewhere  exhibited  extraordinary 
keenness  of  intellectual  perception.  The  authority  of  so  great  a  master  as  Ferrel  perhaps  has 
something  to  do  with  the  fact  that  the  subject  still  remains  obscure.  Most  of  the  errors  have 
been  repeatedly  refuted,  but  the  refutations  fail  to  attract  attention. 


80 

The  fallacy  of  Magnus,  wno  asserte^  that  he  got  an  aosorptiou  of  14.75  per  cent,  from  dry  air,* 
where  Tyndall  found  practically  none,  has  been  abundantly  exposed.  Tyndall  showed  that  the 
glass  plates  which  Magnus  used  to  close  his  glass  vacuum  tube  must  have  been  heated  by 
absorption  of  the  radiation  which  passed  through  them,  acting  thus  as  secondary  sources  of  radia- 
tion, and  that,  being  chilled  by  convection,  their  thermal  effect  was  diminished  on  admission  of 
dry  air.  Tyndall  used  end  plates  of  the  feeble  absorbent,  rock-salt,  whose  thermal  change  was 
relatively  small,  and  this  prevented  the  error  in  question  in  his  measures.  With  the  glass  plates 
used  by  Magnus  the  absorption  of  so  potent  a  substance  as  aqueous  vapor,  being  greatly  masked 
or  reduced  by  the  nontransmissiou  of  radiation  by  glass  in  that  region  where  aqueous  absorption 
is  chiefly  exercised,  was  further  completely  overwhelmed  by  convection,  and  remained  undetected 
from  these  causes,  combined  with  lack  of  sensitiveness  in  the  measuring  apparatus. 

On  the  other  hand,  Tyndall  does  not  completely  meet  the  criticism  that  a  portion  of  the 
absorption  attributed  by  him  to  aqueous  vapor  may  have  been  due  to  a  very  thin  film  of  liquid 
water  condensed  on  the  metallic  reflecting  surface  of  his  tube,  but  contents  himself  with  showing 
that  substantially  the  same  relative  absorptions  were  obtained  when  blackened  tubes  were  used, 
and  finally  with  tubes  so  wide  that  the  radiant  beam  concentrated  by  a  rock-salt  lens  did  not 
touch  the  walls,  so  that  condensation  could  not  have  had  any  material  influence  on  the  result. 
(Contributions,  etc.,  p.  394.)  Magnus,  in  instituting  his  criticism,  overdid  the  matter,  claiming 
that  all  of  the  absorption,  measured  by  Tyudall  and  attributed  by  him  to  aqueous  vapor,  was  due 
to  the  liquid  film.  Lecher  and  Pernter  (Sitzb.  der  A:  Akad.  der  Wissensch.  zu  Wien,  July,  1880; 
Phil.  May.,  (5)  Vol.  11,  p.  1,  Jan.,  1881)  in  repeating  the  charge  have  overlooked  the  experiment 
with  the  rock-salt  lens.  The  claims  so  far  made  rest  upon  mere  assertion,  but  the  following 
considerations,  based  on  internal  evidence  drawn  from  the  experiments  as  published,  indicate  that 
further  elucidation  is  desirable. 

It  is  to  be  remembered  that  in  his  earlier  measures,  owing  to  the  iusensitiveness  of  his  heat- 
measuring  apparatus,  Tyndall  used  a  wide-angled  conical  reflector  to  concentrate  the  rays  upon 
his  thermopile,  and  transmitted  the  radiant  beam  through  polished  tubes  in  order  that  radiation, 
proceeding  from  the  source  under  a  wide  angle,  might  be  fully  utilized  by  multiple  reflections.  Of 
course  the  mean  path. of  the  rays  was  somewhat  longer  than  the  tube. 

Professor  Tyndall  makes  the  following  statement: 

The  absorption  is  exerted  wlien  only  a  small  fraction  of  an  atmosphere  is  introduced  into  the  tube,  and  it  is 
proportional  to  the  quantity  of  air  present.  This  is  shown  by  the  following  table,  which  gives  the  absorption,  by 
humid  air,  at  tensions  varying  from  5  to  30  inches  of  mercury : 

HUMID  AIR. 


Absorption. 

U.6DS1OU. 

Observed. 

Calculated. 

Inches. 

5 

16 

16 

10 

32 

32 

15 

49 

48 

20 

64 

64 

25 

82 

80 

30 

98 

96 

"The  numerical  value  depends  entirely  upon  the  disposition  of  the  apparatus,  and  has  no  connection  with  the 
absorption  of  air.  Thus,  Dr.  Franz,  by  using  a  3-foot  tube  lined  with  black  paper,  which  cut  off  internal  reflection 
and  diminished  the  heating  of  the  glass  end  plates,  had  obtained  an  apparent  absorption  of  3.54  per  cent,  for  dry  air, 
and  Magnus,  with  a  nearly  similar  tube  1  meter  long,  got  2.46  per  cent.,  concerning  which  Tyndall  says :  " Professor 
Magnus  himself  finds  that  the  quantity  of  [radiant]  heat  transmitted  through  his  unblackeued  tube  is  26  times  that 
which  passes  through  his  blackened  one  where  the  oblique  radiation  is  cut  off.  In  the  case  therefore  of  the  naked 
tube,  the  flux  of  [radiant]  heat  sent  down  by  the  heated  glass  plate  adjacent  to  the  lamp,  to  its  fellow  at  the  other 
end,  and  likewise  the  [radiant]  heat  sent  directly  from  the  lamp  to  the  same  plate  are  greatly  superior  to  what  they 
are  in  the  case  of  the  blackened  tube.  The  plate  adjacent  to  the  pile  becomes  therefore  more  highly  heated,  and  as 
its  chilling  is  approximately  proportionate  to  the  difference  of  temperature  between  it  and  the  cold  air,  the  with- 
drawal of  heat  will  be  greatest  when  the  tube  is  unblackened  within.  *  It  is,  I  submit,  not  a  case  of 
absorption,  but  of  direct  chilling  by  the  cold  air."  (Contributions  to  Molec.  Plnjs.,  pp.  419-420.) 


81 

The  third  column  of  this  table  IB  calculated  on  the  assumption  that  the  absorption  is  proportional  to  the  quantity  of 
vapor  in  the  tube,  and  the  agreement  of  the  calculated  and  observed  results  show  this  to  be  the  case,  within  the 
limits  of  the  experiment.  It  can  not  be  supposed  that  effects  so  regular  as  these,  and  agreeing  so  completely  with 
those  obtained  with  small  quantities  of  other  vapors,  and  even  with  small  quantities  of  the  permanent  gases, 
can  be  due  to  the  condensation  of  the  vapor  on  the  interior  surface.  When,  moreover,  5  inches  of  air  were  in  the 
tube,  less  than  one-sixth  of  the  vapor  necessary  to  saturate  the  space  was  present.  The  dryest  day  would  make  no 
approach  to  this  dryness.  Condensation  under  these  circumstances  is  impossible,  and  more  especially  a  condensa- 
tion which  should  destroy,  by  its  action  upon  the  inner  reflector  quantities  of  [radiant]  heat  so  accurately  pro- 
portional to  the  quantities  of  matter  present.  (Heat  Considered  as  a  Mode  of  Motion,  Am.  Ed.,  pp.  405-406, 1869.) 

In  this  quotation  the  air  is  said  to  have  been  humid,  and  yet,  when  reduced  to  a  pressure  of 
one-sixth  of  an  atmosphere,  to  have  contained  "less  than  one-sixth  of  the  vapor  necessary  to 
saturate  the  space."  But  if  the  air  was  anywhere  near  saturation  at  the  ordinary  pressure, 
it  must  have  been  supersaturated  when  reduced  to  a  pressure  of  5  inches,  a  fact  which  was  per- 
fectly well  known  to  Tyndall,  since  he  has  described  it  on  page  46  of  the  same  work.  I  can  only 
reconcile  these  statements  by  supposing  that  either  Tyndall  inadvertently  overlooked  the  increase 
of  relative  humidity  in  air  at  reduced  pressure,  when  writing  this  passage,  or  else  that  the  descrip- 
tion of  the  air  as  "humid"  is  very  misleading;  and  I  submit  that  the  case  is  not  quite  so  axio- 
matic as  its  author  maintained,  and  that  precipitation  of  liquid  water  on  the  inner  walls  of  the 
tube  at  low  pressures,  if  we  take  the  first  horn  of  the  dilemma,  may  have  diminished  the  reflecting 
power  of  the  polished  walls,  while  the  lessening  of  the  vapor  contents  at  the  same  time  would 
render  the  air  more  transmissive,  giving  a  certain  degree  of  compensation  which  is  not  incompat- 
ible with  an  increment  of  vaporous  absorption  by  no  means  proportional  to  the  air  pressure. 

On  page  404  (Heat  as  a  Mode  of  Motion)  we  read : 

The  air  of  the  laboratory  was  dried  and  purified  until  its  absorption  fell  below  unity ;  this  purified  air  was 
then  led  through  a  U-tube  filled  with  fragments  of  perfectly  clean  glass  moistened  with  distilled  water.  Its  neu- 
trality, when  dry,  showed  that  all  prejudicial  substances  had  been  removed  from  it  and  in  passing  through  the 
U-tube  it  could  take  up  nothing  but  the  pure  vapor  of  water.  The  vapor  thus  carried  into  the  experimental  tube 
produced  an  action  ninety  times  greater  than  that  of  the  air  which  carried  it. 

Tyndall  has  pointed  out  (Contributions,  p.  387)  that  merely  letting  dry  air  bubble  through  cold 
water  is  not  a  perfect  means  of  moistening  it,  but  passage  through  U-tubes  filled  with  wet  glass 
is  an  effectual  method  of  producing  saturated  air.  The  moistening  described  on  page  404,  Heat  as 
a  Mode  of  Motion,  is  not  explicitly  stated  to  apply  to  the  conditions  of  the  experiments  with 
"humid"  air  on  page  405;  but  in  the  Contributions  (p.  411)  it  is  stated  the  amount  of  aqueous 
vapor  capable  of  being  taken  up  by  air  at  a  temperature  of  15°  C.,  produced  an  absorbtion  forty 
times  that  of  air;  and  again  (p.  412),  we  read :  "It  is  with  this  common  outer  air,  and  not  with  air 
artificially  saturated  with  moisture  that  I  find  the  absorption  of  aqueous  vapor  to  be  fifty  or  sixty 
times  that  of  the  air  in  which  it  is  diffused."  Numerical  values  depend  upon  absolute  quantities 
of  vapor  and  these  upon  temperatures  and  concomitant  details  which  are  provokingly  infrequent 
in  TyndalPs  memoirs,  but  from  these  supplementary  statements  one  would  infer  that  the  humid 
air  which  gave  an  absorption  of  98  in  the  table  already  quoted,  must  have  been  very  nearly 
saturated,  and  that  the  measures  at  low  pressures  are  open  to  criticism.  Since,  however,  the 
experiments  of  Aitken  show  that  air  which  is  free  from  dust  may  be  supersaturated  without 
precipitation,  I  do  not  mean  to  assert  that  the  precipitation  did  necessarily  occur. 

Abandoning  tubes,  Tyndall  tried  the  method  of  displacing  the  free  air  between  a  cube  of 
boiling  water  and  the  thermopile,  alternately  by  air  dried  by  fresh  chloride  of  calcium  and  by  air 
moistened  by  passing  through  a  cylinder  filled  with  fragments  of  quartz  moistened  with  distilled 
water  (Heat  as  a  Mode  of  Motion,  p.  407),  obtaining  a  differential  deflection  of  about  15°,  corre- 
sponding (by  p.  403,  loc.  cit.)-to  an  aqueous  absorption  of  about  2  percent.  (Temperature  not 
mentioned.) 

Hoorweg  (Pogg.  Ann.,  Bd.  155,  S.  385-402, 1875)  repeated  this  experiment.  No  difference  as 
great  as  0.2"  per  cent,  could  be  found  at  first  between  the  absorption  of  dry  and  moist  air,  as 
exercised  upon  radiation  from  a  Leslie's  tube.  The  transverse  dimensions  of  the  air  blast  are 
not  explicitely  stated,  but  probably  the  air  issued  from  a  narrow  jet.  He  then  repeated  the 
experiment  with  a  moistener  50  cm.  long  and  9  cm.  broad,  obtaining  for  the  absorption  of  moist 
air  1.7  per  cent,  (temperature  9°  C.);  and  finally  with  a  moistener  100  cm.  long  and  9  cm.  broad, 
the  source  being  a  black  copper  plate  heated  by  a  Bunsen  burner,  he  obtained,  with  an  air 
12812— Bull.  G 6 


82 

temperature  of  7°.5  C.,  an  absorption  of  2  per  cent,  by  moist  air,  which  might  perhaps  be  doubled 
by  substituting  a  source  at  100°  C. 

I  fail  to  see  the  cogency  of  some  of  the  remarks  in  this  paper.  The  final  conclusion  in  regard 
to  aqueous  absorption  is  stated  by  this  author  as  follows : 

From  this  I  believe  that  100  meters  of  ordinary  air  are  still  not  by  a  long  way  in  condition  to  produce  the 
results  which  Tyndall  already  obtained  from  10  feet,  namely  that  10  per  cent,  of  the  entering  rays  would  be 
absorbed. 

In  regard  to  this  statement,  I  can  only  say  that  its  truth  or  falsity  depends  upon  what  is  to 
be  understood  by  "ordinary  air."  The  temperature  and  humidity  of  what  would  commonly 
be  considered  as  ordinary  air  vary  so  widely  with  the  locality  and  the  season,  that  without 
numerical  definition  of  water  contents  such  an  assertion  is  too  loose  to  be  of  any  value.  Tyndall's 
statement,*  criticized  in  this  passage,  is  drawn  up  in  the  same  undefined  way  and  is  equally 
devoid  of  meaning,  unless  interpreted  by  other  passages. 

Dr.  H.  Buff  (Pogg.  Ann.,  Bd.  158,  S.  177-213,1876)  used  an  apparatus  patterned  after  that 
of  Magnus  (Pogg.  Ann.,  Bd.  112,  S.  531;  Phil  Mag.  (4),  vol.  22,  p.  85,  1S61),  but  with  a  few  altera- 
tions which  Dr.  Buff  considered  improvements.  In  fact,  results  were  obtained  which  differed  from 
those  of  Magnus,  and  indicated  the  source  of  some  of  his  errors  which  had  already  been  explained 
by  Tyndall.  Dr.  Buff,  however,  appeared  to  think  that  he  had  overcome  these  errors,  whereas  it 
is  evident  that  the  method  as  conducted  by  both  Magnus  and  Buff  is  unsound. 

Instead  of  the  glass-walled  vessel  to  hold  hot  water  which  was  used  by  Magnus,  Buff  had  a 
vessel  of  sheet  brass,  polished  on  the  bottom,  and  radiating  downward  upon  a  thermopile.  Double 
side  walls,  stuffed  with  cotton  wool,  prevented  rapid  cooling.  The  metal  vessel  rested  air-tight  on 
a,  glass  cylinder  20  cm.  high  and  7.5  cm.  wide,  which,  in  turn,  was  made  air-tight  on  the  plate  of 
an  air-pump.  The  thermopile  of  iron  and  germau-silver  wire,  beaten  out  to  a  breadth  of  12.5  mm. 
and  soldered,  was  23  mm.  below  the  heating  surface.  In  the  first  experiments  the  air  was  dried 
by  passing  it  slowly  through  a  40-cin.  tube  of  fused  chloride  of  calcium.  It  is  evident  that  the 
heating  effect  observed  was  a  complex  of  convection,  conduction,  and  radiation  from  a  variety  of 
sources.  The  maximum  deflection,  which  was  attained  after  a  lapse  of  fourteen  to  twenty-two 
minutes,  was  due  mainly  to  slow  heating  of  the  glass  cylinder  by  conduction,  and  to  the  convec- 
tion and  radiation  started  by  the  resulting  disposition  of  heated  walls.  The  effect  continued  for 
thirty  minutes,  although  the  temperature  of  the  hot  water  meanwhile  had  fallen  continuously. 

Dr.  Buff  having  obtained,  as  he  imagined,  a  transmission  of  47.7  per  cent,  from  4.5  cm.  of  dry 
air,  next  increased  his  layer  of  air  to  10  cm.  The  results  were  not  such  as  tp  meet  his  expecta- 
tions. "The  absorptive  power  of  air,  instead  of  proportionately  increasing,  as  I  had  supposed," 
he  says,  "seemed  to  decrease  from  the  50  per  cent,  previously  observed  to  20  and  even  15  per 
cent."  Yet  notwithstanding  this  most  improbable  result,  his  confidence  in  the  accuracy  of  his 
method  and  its  interpretation  (which  differed  in  no  important  respect  from  that  of  Magnus) 
remained  unshaken,  while  Tyndall's  was  branded  as  "unreliable,"  and  these  measures  of  Magnus 
and  Buff  have  been  repeatedly  quoted  as  authoritative,  in  spite  of  their  complete  overthrow  by 
Tyndall. 

Blackening  the  bottom  of  Buff's  brass  vessel  containing  the  hot  water  increased  the  deflec- 
tions "but  feebly,  though  the  radiating  power  of  the  source  of  heat  must  have  been  G  or  7  times 
greater  than  previously ;"  a  result  which  proves  that  only  a  minute  part  of  the  observed  effect  can 
have  been  due  to  the  radiation  of  the  blackened  brass,  and  which  consequently  demonstrates  that 
the  large  variations  observed  were  at  any  rate  not  due  to  absorption  of  radiation  by  the  inclosed 
gases. 

Only  one  other  point  in  this  paper  requires  mention,  namely,  the  assertion  that  a  plate  of 
rock-salt,  0.3  cm.  thick,  absorbs  40  per  cent,  of  the  radiation  from  a  vessel  of  hot  water,  and  that 

*  "Eegarding  the  earth  as  a  source  of  heat  no  doubt  at  least  10  per  cent,  of  its  [radiant]  heat  is  intercepted 
within  10  feet  of  the  surface."  (Heat  as  a  Mode  of  Motion,  p.  404.)  It  is  to  be  borne  in  mind  that  this  refers  espe- 
cially to  radiation  from  a  surface  which  is  commonly  moist  and  that  such  radiation  through  nearly  saturated  surface 
layers  of  air  may  be  especially  obstructed  by  aqueous  vapor.  (See  Contributions,  p.  395,  and  this  bulletin,  p.  90 
to  106.1 


83 

the  therinoclirose  of  rock-salt  and  dry  air  are  similar,*  Buff  maintaining  that  Tyndall  found  no 
absorption  by  air  because  bis  rock-salt  plates  bad  already  sifted  out  the  rays  for  \vhich  air  is 
opaque.  Pi-ofessor  Tyndall,  in  bis  reply  (Proc.  Royal  Soc.  London,  vol.  30,  p.  10,  Dec.,  1879), 
points  out  that  be  bad  already  (see  Heat  as  a  Node  of  Motion,  p.  399)  tried  the  experiment  of 
bringing  the  naked  face  of  his  thermopile  "within  one-twentieth  of  an  inch  of  [the]  terminal  plate 
of  rock-salt.  There  was  not  the  slightest  alteration  of  the  previously  obtained  result.  Dry  air,  as 
before,  behaved  like  a  vacuum."  The  course  of  the  radiation  was  here  through  a  succession  of 
vacuum,  salt,  vacuum  (or  dry  air  at  pleasure),  salt,  and  one  twentieth  inch  of  normal  air  to  the 
pile.  There  was  little  probability  that  so  thin  a  layer  of  air  as  one-twentieth  inch  could  sift  out 
and  totally  remove  any  appreciable  amount  of  a  special  class  of  rays;  and  Melloni's  measurement, 
which  made  the  transmission  of  a  plate  of  rock-salt,  0.26  cm.  thick,  as  great  as  92.3  per  cent,  of  the 
total  radiation,  almost  all  of  the  loss  being  due,  not  to  absorption,  but  to  nonselective  surface 
reflection,  might  well  have  been  deemed  sufficient  to  prove  the  fallacy  of  Buff's  suggestion  that  a 
few  cm.  of  air  or  a  small  fraction  of  a  cm.  of  rock-salt  can  totally  remove  a  large  percentage  of 
the  radiation;  but  to  put  the  matter  beyond  all  possible  doubt,  Tyndall  constructed  a  new  appa- 
ratus (loc.  cit.,  fig  1,  p.  16)  placing  the  thermopile  in  a  chamber  filled  with  hydrogen,  protecting 
against  hydrogen  convection  currents  and  radiation  from  side  walls  by  diaphragms,  and  intro- 
ducing a  central  variable  chamber  containing  dry  air,  in  which  the  thickness  of  the  air  layer  could 
be  varied  from  zero,  when  the  inclosing  rock-salt  plates  were  in  contact,  to  3  inches,  "which 
exceeds  by  more  than  50  per  cent,  the  thickness  of  the  layer  to  which  Professor  Buff  ascribes  ail 
absorption  of  50  or  60  per  cent."  "Repeated  experiments  with  this  apparatus  proved  the  absorp- 
tion of  the  layer  of  dry  air  in  the  chamber  to  be  nil." 

The  supposition  of  an  identical  absorption  by  rock-salt  and  air  was  then  tested  by  comparing 
the  transmission  of  a  thick  plate  of  rock-salt  in  vacuum  with  its  transmission  in  air.  There  was  no 
sensible  difference.  There  is  consequently  no  similarity  in  the  therrnocbrose  of  air  and  rock-salt. 

•Finally,  Tyndall  shows  that  Buff's  method,  although  defective  "even  when  every  care  is 
bestowed  upon  it,"  may  be  improved.  "A  glass  cylinder,  12  inches  long  and  2f  inches  in  diameter, 
is  mounted  on  the  plate  of  an  air-pump.  On  it  is  placed  a  tin  vessel  with  a  brass  bottom,  intended 
to  contain  the  water  which  warms  the  bottom  or  source  of  heat.  A  thermopile  is  mounted  on  the 
air-pump  plate  on  which  the  cylinder  stands,  one  of  its  faces  being  presented  to  the  bottom  of  the 
tin  vessel.  The  conical  reflector  is  abandoned,  a  piece  of  tubing,  blackened  within,  aud  intended 
to  cut  off  the  radiation  from  the  sides  of  the  vessel,  being  pushed  over  the  pile.  Instead  of  bring- 
ing brass  and  glass  into  direct  contact,  as  in  the  apparatus  of  Professor  Buff,  a  washer  of  non- 
conducting india  rubber,  an  inch  and  an  eighth  in  thickness,  separates  the  one  from  the  other. 
There  is  no  chilling  by  cold  water,  and  the  distance  of  the  pile  from  the  source  renders  it  difficult 
for  heat  to  pass  by  convection  from  the  one  to  the  other."  With  this  apparatus,  instead  of  finding 
olefiant  gas  more  diatherinaut  than  air,  as  Buff  had  done,  Tyudall  obtained  an  absorption  of  33 
per  cent,  from  a  depth  of  11  inches  of  olefiaut  gas,  while  air  and  hydrogen  did  not  differ  appreci- 
ably from  a  vacuum  in  their  readiness  of  transmission.  The  results  agree  with  Tyndall's  earlier 
measures  obtained  by  other  methods. 

It  might  be  supposed  that  such  a  complete  exposure  of  the  fallacy  of  Magnus'  method,  both 
in  its  original  form  and  as  modified  by  Professor  Buff,  would  forever  settle  the  questions  at  issue; 
and  that  Buff's  further  statement  that  be,  like  Magnus,  found  no  difference  between  the  absorp- 
tion of  dry  aud  moist  air  would  be  taken  for  what  it  is  worth,  namely,  nothing  at  all;  but  such 
statements  as  those  quoted  from  Ferrel,  made  six  years  after  this  crushing  rejoinder,  show  that 
old  errors  die  bard. 

Prof.  W.  M.  Davis,  in  his  Elementary  Meteorology  (p.  145,  Boston,  1894),  says: 

The  action  of  water  vapor  on  insolation  and  terrestrial  radiation  has  been  much  discussed.  Some  have  regarded 
it  as  diathermanous  to  insolation,  but  relatively  opaque  to  terrestrial  radiation,  and  have  therefore  attributed  to  it 
a  controlling  influence  in  determining  the  temperature  of  the  atmosphere.  More  careful  experiments  have,  however, 
shown  that  water  in  the  truly  vaporous  state  is  as  diathermanous  as  pure  dry  air  to  terrestrial  radiation;  and  that 
it  is  only  water  in  the  liquid  state  that  exerts  a  strong  control  over  radiation  from  the  earth.  This  appears  to  be 
confirmed  by  observations  on  the  diurnal  range  of  temperature  under  varying  conditions  of  humidity.  If  the 


*  It  will  be  shown  subsequently  (p.  114)  that  there  is  an  analogy  between  the  radiant  powers  of  rock-salt  and 
dry  air,  but  not  identity. 


84 

temperature  of  the  air  is  well  above  saturation,  the  range  is  relatively  strong;  if  near  saturation,  the  range  is 
diminished,  even  though  no  visible  clouding  of  the  sky  occurs;  if  a  thin  hazy  cloud  is  formed,  the  range  is  greatly 
reduced. 

The  experiments  which  have  been  interpreted  in  favor  of  the  diathermancy  of  water-vapor 
have  been  refuted  long  ago,  and  Professor  Davis,  since  the  publication  of  his  book,  has  given 
evidence  that  he  no  longer  adheres  to  the  erroneous  doctrine  there  enunciated.  (See  his  "Absorp- 
tion of  Terrestrial  Kadiation  by  the  Atmosphere,"  Science,  N.  S.  Vol.  2,  p.  485,  Oct.  11,  1895.) 
The  diminution  of  the  daily  range  of  temperature  with  a  clear  sky,  as  saturation  approaches,  is  to 
be  attributed  partly  to  a  change  in  the  quality  of  aqueous  absorption,  but  also  to  the  increase  of 
water- vapor  and  its  ascent  to  exceptional  heights  in  the  atmosphere  in  considerable  quantity, 
whereby  the  escape  of  surface  radiation  is  impeded  by  the  strong  aqueous  absorption  of  the  infra- 
red rays,  especially  for  those  between  5/<  and  8/<,  not  far  from  the  point  where  the  maximum  energy 
in  the  radiation  from  bodies  at  ordinary  temperatures  resides.  The  presence  of  large  masses  of 
water-vapor  in  the  upper  air  may  not  always  be  indicated  by  high  relative  humidity  at  the  sur- 
face, any  more  than  by  clouds,  but  it  is  evidenced  by  the  strengthening  of  the  rain-band,  as  seen 
in  the  spectroscope,  as  well  as  by  the  diminution  of  the  diurnal  range  of  temperature;  and  after 
heavy  rainfall  has  depleted  the  upper  air  of  moisture,  the  direct  rays  of  the  sun  are  intensified, 
and  to  a  still  greater  degree  the  loss  of  heat  by  radiation  from  the  earth's  surface,  so  that  the 
change  of  temperature  between  day  and  night  reaches  its  greatest  value,  and  at  the  same  time 
the  rain-band  fades  out,  showing  that  it  is  the  withdrawal  of  the  invisible  veil  of  water-vapor 
which  has  increased  both  radiation  and  daily  range.  The  statement  on  page  32  of  Professor 
Davis'  book  that  "water  vapor  is,  like  clear  air,  a  poor  absorber  of  nearly  all  kinds  of  waves," 
and  the  doubt  which  is  cast  upon  the  theory  that  the  atmosphere  is  a  trap  which  allows  solar  rays 
to  enter  more  freely  than  surface  rays  are  permitted  to  escape,  are  both  overthrown  by  the  expert- 
mental  demonstration  of  the  efficacy  of  aqueous  vapor  as  an  absorbent  of  infra-red  rays. 

Prof.  Thomas  Preston  in  his  Theory  of  Heat  (p.  485,  London,  1894)  says  in  introducing  the 
experiments  of  Lecher  and  Pernter  (published  in  1880) :  "But  these  new  investigations,  instead  of 
settling  the  question  in  dispute  between  Tyudall  and  Magnus  as  to  the  comparative  absorptions 
of  dry  and  morst  air,  place  the  whole  matter  in  a  state  of  greater  uncertainty.  For  whereas  Tyn- 
dall  found  an  exceedingly  low  absorption  for  dry  and  a  high  absorption  for  moist  air,  while  Mag- 
nus found  the  same  absorption  for  both,  and  that  tolerably  high,  the  results  of  the  experiments  of 
Lecher  and  Pernter  show  practically  no  absorption  for  either;  or,  in  other  words,  both  dry  and 
moist  air  act  as  a  vacuum  toward  radiant  heat."  These  and  numerous  other  less  explicit  state- 
ments in  current  scientific  literature  show  that  even  down  to  the  present  day  the  question  of  the 
action  of  aqueous  vapor  upon  telluric  radiation  is  still  regarded  by  many  as  an  open  one. 

I  proceed  to  the  discussion  of  the  last-named  observations,  which  contain  some  puzzling  but 
not  inexplicable  features.  Lecher  and  Pernter  (Sitzb.  tier  A;.  AJcad  der  Wiss.  zu  Wien,  July,  1880; 
Phil.  Mag.  (5),  vol.  11,  p.  1,  Jan.,  1881)  by  substituting  a  thin  horizontal  plate  of  lampblacked 
copper  brought  suddenly  to  100°  C.  by  a  jet  of  steam,  in  place  of  the  arched  dome  of  glass  heated 
by  hot  water  in  the  original  apparatus  of  Magnus,  succeeded  in  shortening  the  time  of  exposure 
and  diminishing  the  convection  until  they  were  able  to  confirm  Tyndall's  observation  of  the  sen- 
sibly perfect  transmission  of  radiation  by  dry  air.  But  with  a  layer  of  31  cm.  of  air  they  could 
detect  no  difference  between  the  absorption  of  moist  air  and  dry.  Magnus'  galvanometer  and 
thermopile  were  too  insensitive  to  measure  this  difference,  even  if  his  arrangement  had  been  free 
from  its  other  defects ;  but  Lecher  and  Pernter's  instruments  apparently  had  the  requisite  delicacy, 
and  we  must  seek  elsewhere  for  the  cause  of  their  failure. 

The  face  of  the  thermopile  was  covered  with  lampblack,  which  is  very  hygroscopic,  "and  like- 
wise the  bottom  of  the  radiating  vessel.  Whenever  this  was  heated  in  moist  air  and  in  a  closed 
vessel,  moisture  was  driven  off  from  the  coating  of  the  radiator  and  probably  deposited  to  a  suffi- 
cient extent  upon  the  blackened  thermopile  to  largely  compensate  by  the  development  of  latent 
heat  for  the  slight  diminution  of  radiation  by  only  a  few  inches  of  moist  air,  while  the  radiation  of 
the  hot  vapor  (diminished  by  aqueous  absorption)  was  added  to  that  of  hot  metal.  The  short  time 
of  exposure  (90  sec.)  diminished  the  influence  of  convection  currents,  but  favored  the  inclusion  of 
a  transitory  phenomenon,  like  the  evaporation  of  hygroscopically  imbibed  moisture. 

The  importance  which  has  been  attributed'  to  the  observation  makes  it  desirable  to  analyze  it 


85 


somewhat  critically.  Comparing  measurements  of  the  absorption  of  various  gases  and  vapors  by 
Lecher  and  Pernter  with  those  made  on  the  same  substances  by  Tyndall,  it  will  be  seen  that  the 
differences  between  their  results  for  the  absorption  exercised  on  the  radiation  from  a  blackened 
metal  plate  at  100°  C.  are  too  large  to  be  neglected,  and  in  the  case  of  vapors  the  discrepancies 
are  excessive,  as  the  following  table  shows : 

TABLE  53. 


Lecher  and  Pernter. 

Tyndall. 

Length. 

Pressure.  Absorption. 

t. 

Length. 

Pressure. 

Absorption. 

t. 

(t) 

| 

CHI. 

mm. 

cm. 

mm. 

Chloroform,  CHC13 
Ether,  (C2H6)jO 

31 
31 

70 
13 

0.0050 
0.  0504 

'"  - 

126 
126 

13 
13 

*  0.  216 
*  0.541 

Source 
(  inno 

Benzole,  CriH6 

31 

42 

0.0619 

•  g  =    •            126 

13 

*  0.  345 

Ethylene,  C>H4 
Carbon  monoxide,  CO 

31 
31 

751 
744 

0.  4826 
0.  0660 

s'ol  '        5 

762 
762 

1  0.  328 
1  0.  068 

[Source 
1  270° 

0.551 
0.076 

Carbon  dioxide,  CO2 

31 

748 

0.  0810 

g                       5           762 

1  0.  076 

0.094 

*  Heat  as  a  jlode  of  Motion,  p.  441.    (Conditions  described  p.  431.) 
t  Contributions  to  molecular  Physics,  p.  170. 

*  Temperature  of  source  100°  C.    Masses  of  gas  equivalent  to  those  in  the  experiments  of  Lecher  and  Pernter. 

To  account  for  their  discrepancies  Professors  Lecher  and  Pernter  refer  to  observations  of  Beg- 
nault  (Mem.  de  VAcad.  JV.,  t.  26).  "Regnault  has  observed  that  the  tension  of  vapors  is  less  in 
vacuum  than  in  a  space  filled  with  air,  and  he  explains  this  as  the  result  of  condensation  on  the 
walls.  This  causes  a  diminution  of  the  vapor  tension,  so  that  while  in  a  vacuum  compensation  is 
instantly  made  by  the  liquid,  in  a  space  filled  with  air  this  requires  time,  and  the  full  vapor 
tension  is  never  reached."*  How,  in  the  cases  cited  Tyndall  employed  an  exhausted  tube,  into 
which  his  vapors  were  allowed  to  expand  from  a  sample  tube  connected  with  a  vapor  flask,  the 
vaporization  being  made  "without  the  slightest  ebullition"  (Contributions  to  Molec.  Phys.,  p.  179), 
but  since  there  were  no  special  precautions  to  keep  all  parts  of  the  vapor  chambers  at  the  same  tem- 
perature, it  is  conceivable  that,  on  the  opening  of  the  vapor  flask  into  the  sample  tube,  a  portion  of 
vapor  condensed  on  the  walls  of  the  latter,  and  subsequently,  when  the  lower  valve  was  closed 
and  the  upper  opened,  this  condensed  liquid  evaporated  into  the  absorption  tube.  Thus  there 
may  have  been  a  larger  quantity  of  vapor  present  in  the  absorption  tube  than  might  have  been 
expected  from  the  temperature  of  evaporation.  In  this  way  we  may  explain  the  fact,  commented 
on  by  Lecher  and  Peruter,  that  the  pressure  in  the  vapor  flask,  computed  from  Tyndall's  data, 

*  This  statement  hardly  expresses  the  facts  of  the  original  observations  which  are  contained  in  Me"moires  de 
1'J.cadernie  des  Sciences  de  I'Institut  Imperial  de  France,  t.  26,  p.  700,  Paris,  1862.  Regnault  found  that  the  density 
of  aqueous  vapor,  relatively  to  that  of  air,  increases  as  the  saturation  point  is  approached. 


Relative  hu- 
midity. 

Relative  den- 
sity of  aque- 
ous vapor. 

Relative  hu- 
midity. 

Relative  den- 
sity of  aque- 
ous vapor. 

Per  cent. 

Per  cent. 

100 

0.  64693 

87.0 

0.  62499 

96.4 

0.  63849 

73.3 

0.  62140 

96.4 

0.  62786 

30.2 

0.  62078 

Regnault  himself  says  (p.  701) :  "  The  experiments  which  have  been  made  at  temperatures  very  near  those  of 
saturation  give  densities  larger  [than  the  theoretic  density],  and  the  difference  is  so  much  the  greater  as  we 
approach  nearer  saturation.  I  conclude  from  this  that  the  density  of  the  vapor  of  water,  in  the  vacuum  and  under 
feeble  pressures,  may  be  calculated  after  the  law  of  Mariotte  and  according  to  the  theoretic  density,  provided  the 
fraction  of  saturation  does  not  surpass  0.8,  but  that  this  density  increases  notably  toward  the  state  of  saturation. 
This  last  circumstance  may  be  due  to  two  causes :  either  the  vapor  of  water  experiences,  really,  an  abnormal  con- 
densation on  approaching  the  state  of  saturation,  or  else  a  part  of  the  water  remains  condensed  upon  the  glass 
walls  and  only  takes  the  gaseous  state  when  the  interior  vapor  is  far  from  saturation." 

Lecher  and  Pernter  ignore  Regnault's  first  explanation  that  aqueous  vapor  becomes  abnormally  condensed  on 
approaching  the  point  of  saturation,  but  it  will  be  shown  subsequently  that  this  condensation  is  a  fact. 


86 


approaches  the  boiling  point  of  the  volatile  liquid  in  several  instances,  whereas  the  experiments 
were  actually  conducted  at  a  much  lower  temperature.  But,  admitting  the  truth  of  this  part  of 
the  criticism  and  the  uncertainty  of  the  vapor  densities  computed  from  the  relative  volumes  of 
sample  and  absorption  tubes,  the  argument  does  not  apply  to  experiments  (such  as  those  quoted 
in  Table  53)  in  which  the  vapor  pressures,  measured  by  a  manometer,  fell  far  short  of  those  for 
saturation  at  the  presumed  temperature.  Tyndall  is,  unfortunately,  very  seldom  explicit  in 
describing  his  conditions  of  experiment,  but  it  may  be  inferred  from  some  of  his  statements  that 
the  temperature  of  his  apparatus  was  in  general  that  of  the  apartment,  and  not  far  from  15°  C., 
at  which  temperature,  and  under  complete  absence  of  air,  it  is  improbable  that  there  can  have 
been  any  appreciable  liquid  films  condensed  from  the  vapors  in  question.  Moreover,  the  point 
can  be  subjected  to  a  much  more  severe  test. 

Tyndall,  in  his  Contributions  (p.  171),  gives  a  series  of  measurements  in  which  not  the  vapor 
pressure,  but  the  thickness  of  a  layer  of  air  saturated  with  ether- vapor,  was  varied.  Here,  if  the 
absorption  had  been  due  to  a  film  of  liquid  ether  condensed  on  the  rock-salt  plates,  the  mere  vari- 
ation in  the  distance  between  these  plates  could  have  had  no  effect  upon  the  transmitted  radiation. 
In  the  next  table  Tyndall's  results  are  given  in  comparison  with  a  series  by  Lecher  and  Pernter,  in 
which,  however,  it  is  the  pressure  of  the  ether- vapor  which  has  been  varied.  Whether  it  is  per- 
missible to  make  comparison  under  these  circumstances  will  be  considered  presently.  The 
temperature  in  Lecher  and  Pernter's  experiment  was  7°.4  C.,  which  fixes  the  pressure  attainable 
at  the  upper  limit  at  a  figure  probably  lower  than  Tyndall's;  but  since  Tyndall's  greatest  depth  of 
air  and  saturated  ether- vapor  was  only  one-sixth  of  that  used  by  Lecher  and  Pernter,  the  latter 
ought  still  to  have  had  the  greater  absorption;  nevertheless,  according  to  their  determination,  the 
absorption  was  actually  less.  In  Table  51,  Zis  the  length  of  the  absorbent  column,  p  is  the  pres- 
sure of  the  ether- vapor,  t  is  the  fraction  of  radiation  from  a  lampblack  surface  transmitted  by  the 
ethyl  ether,  x  is  the  exponential  coefficient  of  transmission  in  the  formula, 

t  =  e~mx 

where  e  is  the  Naperian  base,  and  m  is  the  mass  of  absorbent  vapor  in  a  column  of  unit  section. 
Without  further  data  no  absolute  comparison  is  possible,  but  since  m  is  proportional  to  7p,  and  I 
in  the  one  case  is  constant  and  equal  to  31  cm.,  p  being  constant  in  the  other  case,  and  probably 
about  35  cm.,  or  nearly  the  same,  p  and  I  may  be  taken  respectively  in  place  of  m  in  a  preliminary 
computation  of  a  multiple,  nx,  differing  only  slightly  from  x. 

TABLE  54. — Ether-vapor. 


Tyndall. 

Lecher  and  Pernter. 

I 

P                  IP 

t 

nx  for  1  cm.  I 

I 

f 

lp 

t 

nxtorlna.p 

em. 

cm. 

cm. 

cm. 

0.127 

35  ? 

4.45 

0.979 

0.  1672 

31 

1.28 

39.68 

0.  9496 

0.  0404 

0.254 

35  ? 

8:89 

0.954 

0.  1854 

31             4.  12 

127.  72 

0.  8737 

0.  0328 

0.508 

35? 

17.78 

0.913 

0.  1792 

31 

7.86 

243.  66 

0.  7794 

0.  0317 

1.  016 

35  ? 

35.  56 

0.857 

0.  1519 

31 

12.52 

388.12 

0.  6924 

0.  0294 

2.032 

35  ? 

71.12 

0.790 

0.  1160 

31 

23.33 

723.  23 

0.  5859 

0.  0229 

3.810 

35  ? 

133.  35 

0.  654 

0.  1115 

5.080 

35  ? 

177.  80 

0.649 

0.  0851 

For  equal  masses  of  ether- vapor  the  absorption  and  the  exponential  coefficient  are  consider- 
ably larger  in  Tyndall's  series  than  in  that  of  Lecher  and  Peruter;  but  in  both  the  value  of  x 
increases  as  the  absorbent  mass  diminishes,*  and  in  nearly  the  same  ratio,  Tyudall's  rate  being 
slightly  the  greater.  Thus,  Tyndall's  measures  show  that  with  a  variation  of  the  mass  in  the 
ratio,  1:20.00,  there  is  a  change  in  x  in  the  ratio,  1:0.4590,  while  Lecher  and  Pernter,  for  a  mass 
change  in  the  ratio,  1:18.23,  have  a  variation  of  x  in  the  ratio  1:0.5673.  From  the  result  of  this 
test,  I  think  it  can  not  be  denied  that  the  absorption  by  a  vapor  measured  by  Tyndall  is  genuine. 
Lecher  and  Pernter  have  also  been  measuring  an  effect  which  depends  on  the  amount  of  vapor 


*  Lecher  and  Pernter  say:  "  x  always  becomes  smaller  as  the  thickness  of  the  layer  becomes  smaller/''  which  is 
obviously  erroneous. 


87 


present,  and  where  their  results  deviate  from  those  of  Tyndall  it  is  owing  to  the  defects  of  their 
method.  It  seems  to  me  that  the  capacity  of  lampblack  for  condensing  vapors  to  the  liquid  state, 
and  absorbing  them  in  its  pores,  is  partly*  responsible  for  the  apparent  inactivity  of  aqueous 
vapor  in  Lecher  and  Pernter's  experiments  by  the  compensation  already  explained;  and  it  is  note- 
worthy that  their  deviations  from  Tyudall  are  greatest  in  the  case  of  the  more  condensible  vapors, 
while  for  the  permanent  gases  there  is  approximate  agreement,  especially  if  the  comparison  be 
made  between  the  absorption  of  equal  masses t  exercised  on  radiation  from  the  same  source. 
This  has  been  done  in  the  last  column  of  Table  53  for  the  three  permanent  gases  by  interpolating 
values,  for  a  pressure  of  7.~>  inches  of  mercury,  from  Tyndall's  Contributions  to  Molecular  Physics, 
Table  XX,  p.  37,  for  COj,  and  Table  I,  p.  22,  for  C2H4,  assuming  that  the  total  radiation  is  repre- 
sented by  the  mean  of  the  values  on  pages  18  and  19,  or  334  units.f  The  figures  for  CO  are 
obtained  in  the  same  way  from  Table  XIX,  p.  30.  The  pressure  selected  §  is  such  as  to  give  an 
absorbent  mass  nearly  identical  with  that  of  Lecher  and  Pernter.  The  result  indicates  that, 
where  the  physical  state  remains  unchanged,  it  is  permissible  to  compare  the  effects  of  equivalent 
masses  even  under  diverse  conditions  of  pressure  or,  in  other  words,  it  is  the  number  of  molecules 
encountered  in  passing  through  a  given  gas  which  determines  the  absorption  of  radiation. 

From  certain  discrepancies  in  the  relative  positions  of  absorbent  vapors  in  Tyndall's  lists 
Lecher  and  Peruter  deduce  a  variation  of  some  30  per  cent,  between  the  results  from  black  and 
from  polished  tubes,  and  conclude  that  the  unconformities  which  Tyndall  attributed  to  impurities 
in  his  substances  are  really  due  to  the  variable  proportion  in  which  the  transmission  through  a 
film  of  liquid  adhering  to  the  walls  and  the  direct  transmission  through  vapor  enter  into  the 
results,  according  as  a  reflecting  or  a  nonreflecting  tube  is  employed.  The  criticism,  however,  is 
hardly  conclusive,  especially  since  they  found  their  remarks  on  some  of  Tyndall's  earlier  measures 
in  which  the  probable  error  of  observation  was  large. 

Finally,  while  themselves  recognizing  that  transmission  must  be  expressed  by  an  exponential 
formula, 

t  =  e  -  mx 

in  which,  unless  the  radiation  be  homogeneous,  x  varies  as  a  complex  function  of  m  (the  absorbent 
mass),  any  constant  exponential  coefficient  being  inapplicable  to  cases  of  absorption  where  par- 
ticular rays  are  constantly  dropping  out,  because  totally  extinguished,  the  authors  fail  to  apply 
their  knowledge  where  it  is  peculiarly  needed,  namely,  in  treating  Yiolle's  comparison  of  solar 
radiation  at  the  top  and  bottom  of  Mount  Blanc.  They  rightly  conclude  that  the  absorption  of 
16  per  cent,  exercised  on  the  solar  rays  by  a  layer  equivalent  to  2,428  meters  of  air  at  normal 
pressure,  and  having  a  pressure  of  water- vapor  of  5.3  mm.  at  the  bottom,  must  have  been  largely 
due  to  the  aqueous  absorption;  but,  applying  an  erroneous  formula,  they  then  deduce  a  mean 

*  It  is  evident  that  if  the  explanation  given  here  is  correct  the  numerical  result  must  also  depend  in  part  upon 
the  dimensions  of  the  apparatus. 

t  Tyndall  (Heat  as  a  Mode  of  Motion,  p.  433-435)  has  given  an  argument  which  proves  that  equivalent  absorb- 
ing masses  must  be  used,  if  the  relative  absorptions  of  dift'erent  liquids  and  vapors  are  to  be  compared. 

tFrom  the  explanation  of  the  calibration  of  the  galvanometer  (pp.  17-19),  and  from  the  values  juxtaposed  in 
Tyndall's  Tables  I,  III,  and  elsewhere,  it  is  evident  that  the  quantities  labeled  "  absorption  per  100 "  are  not  per- 
centages, but  absorptions  stated  in  terms  of  forces,  corresponding  to  galvanometer  deflections,  as  read  from  a  curve 
of  calibration. 

$  The  values  for  the  interpolation  curve,  in  the  case  of  carbon  dioxide  (4-foot  layer,  temperature  of  source  10(P 
C.,  Joe.  clt.,  p.  15),  follow  : 


Pressure       Absorption 
(obs.). 

Absorption 
(inter- 
polated). 

Pressure. 

Absorption 
(obs.). 

Absorption 
(inter- 
polated). 

Inches.          Per  c<tnt. 

Per  cent. 

Inches. 

Per  cent. 

Per  cent. 

0.5 

1.50 

1.8 

3.0 

6.53 

5.8 

1.0 

2.25 

3.0 

3.5 

7.34 

6.3 

1.5             3.14 

3.8  i 

5.0 

7.49 

7.8 

2.0 

4.19 

4.5  ! 

10.0 

10.78 

11.3 

2.5 

5.33 

» 

15.0 

14.37 

13.9 

88 

absorption  of  0.007  per  cent,  by  1  meter  of  air  of  the  given  humidity  and  for  sunshine,  and  compare 
this  with  Tyndall's  absorption  of  radiation  from  a  low-temperature  source  by  a  fresh  layer  of  moist 
air,  leaving  the  inference  that  this  measurement — several  hundred  times  greater  than  that  com- 
puted on  their  assumption — must  necessarily  be  wrong.  This  reasoning  is  quite  inadmissible. 
In  sunshine  the  rays  absorbable  by  water  form  but  a  small  part  of  the  total  radiation,  while  in 
the  low- temperature  sources  employed  by  Tyndall  they  constitute  the  larger  part.  Besides  this, 
the  principal  part  of  the  absorption  is  exercised  by  the  first  few  meters  of  moist  air  or  their 
equivalent.  It  is  perfectly  safe  to  say  that  eveu  at  the  summit  of  Mount  Blanc  an  amount  of 
aqueous  vapor  had  already  been  traversed  many  times  exceeding  that  in  Tyndall's  meter  or  there- 
abouts of  moist  air,  and  that  a  large  part  of  the  rays  for  which  aqueous  vapor  is  especially 
opaque  and  whose  absorption  was  measured  by  Tyudall  had  already  been  sifted  out.  The  reasoning 
by  which  Professors  Lecher  and  Pernter  support  their  failure  to  detect  any  absorption  from  moist 
air  is,  therefore,  not  justified. 

Tyndall's  last  contribution  to  this  subject  is  a  paper  on  "The  action  of  free  molecules  on 
radiant  heat  and  its  conversion  thereby  into  sound"  (Phil.  Mag.  (5),  vol.  13,  pp.  435-462,  and  480- 
526,  May  and  June,  1882).  It  contains  a  variety  of  incidental  results  which  have  a  bearing  on 
questions  which  have  arisen  in  connection  with  the  present  research.  The  beginning  of  the  paper 
gives  an  excellent  historical  summary  of  the  Tyndall-Magnus  controversy.  On  pages  455-456  we 
read  concerning  Magnus'  experimental  determination  of  the  radiation  from  heated  gases  passed 
through  a  hot  tube  15  mm.  in  diameter,  bent  up  at  the  end,  so  that  the  vertical  current  ascended 
400  mm.  in  front  of  the  pile: 

"When  dry  air  was  sent  through  this  tube  the  deflection  produced  was  three  divisions  of  a  scale;  when  air 
which  had  passed  through  water  at  a  temperature  of  15°  C.  was  sent  through  the  tube  the  deflection  rose  to  5  div. ; 
when  the  water  was  warmed  to  60°  or  80°  F.  the  deflection  was  20  div. ;  and  when  the  water  boiled  the  deflection 
was  100  div.  In  this  last  experiment,  however,  a  mist  appeared,  so  that,  as  urged  at  the  time,  the  radiation  could 
not  be  said  to  have  been  purely  from  vapor.  In  the  other  case  no  mist  was  visible,  but  it  was  nevertheless  concluded 
that  the  20-div.  deflection  was  due  to  the  formation  of  mist  at  the  boundary  of  the  ascending  current. 

Tyndall  concludes  that  the  first  deflection  came — 

Not  from  dry  air,  but  from  the  adjacent  aqueous  vapor  which  had  been  warmed  by  the  dry  air. 

That  the  deflection  in  the  second  experiment  was  small  is  not  surprising.  The  radiation  which  could  reach  the 
pile  from  a  jet  of  air  only  15  mm.  in  diameter,  and  containing  such  moisture  as  could  be  taken  up  at  15°  C.,  must 
have  been  extremely  small  under  any  circumstances.  But  in  the  present  case  eveu  this  small  radiation  was 
diminished  by  the  passage  of  the  [radiant]  heat  through  400  mm.  of  undried  air.  I  should  demur  [says  Tyndall] 
to  the  explanation  of  the  third  experiment  and  question  the  warrant  to  imagine  a  mist  which  could  not  be  seen. 
Even  the  fourth  experiment  where  mist  was  visible,  yielded,  I  doubt  not,  a  mixed  result,  part  of  the  effect,  and  probably 
the  smallest  part,  being  due  to  the  mist,  and  part  of  it  to  the  vapor. 

On  pages  483-484  Tyndall  refers  to  his  own  experiments  on  the  transmission  of  a  parallel 
beam  of  radiation  from  a  rock-salt  lens,  described  in  his  Contributions  (p.  394),  and  says  that  the 
tube  was  rough  brass,  tarnished,  and  that  the  heating  of  the  tube  from  air  dynamically  heated  by 
compression,  and  from  the  partial  condensation  of  vapor  on  the  walls  of  the  tube  when  the  air 
was  moist,  produced  a  small  radiation  from  its  inner  surface  which  disturbed  the  result.  Hence 
in  his  new  apparatus  the  interior  of  the  tube  was  silvered  and  polished. 

The  absorptions  measured  by  Tyudall  are  greater  when  the  source  is  a  slowly  vibrating  or 
low-temperature  one,  except  in  the  case  of  absorption  by  carbon  dioxide ;  but  if  the  apparatus 
could  be  made  sensitive  enough  to  work  with  a  very  low-temperature  source  of  radiation  whose 
spectral  maximum  should  be  at  a  longer  wave-length  than  the  region  of  especial  absorption,  the 
result  found  for  carbon  dioxide  would,  no  doubt,  be  the  general  one. 

The  radiation  from  a  hydrogen  flame  proceeds  principally  from  highly  heated  vapor  of 
water  and  its  absorption  by  38  inches  (96.5  cm.)  of  air  at  60°  F.,  saturated  with  moisture  and  con- 
taining an  amount  of  water-vapor  equivalent  to  a  liquid  layer  0.001  271  cm.  deep,  was  found  to  be 
10.7  per  cent.,  while  dry  air  produced  no  measurable  absorption. 

The  thin  liquid  films  produced  by  condensation  of  vapors  on  rock-salt  plates  when  the  con- 
centrated vapors  were  allowed  to  flow  over  a  plate  placed  in  the  path  of  the  radiant  beam  were 
found  to  have  no  effect  on  transmission,  unless,  as  in  breathing  on  a  plate,  the  film  amounted  to  a 


89 

visible  wetting ;  but  if  the  plate  was  put  iu  contact  with  the  pile  the  liberation  of  latent  heat  in 
the  act  of  condensing  from  vapor  to  liquid  produced  powerful  deflections. 

The  assumption  that  absorption  depends  upon  the  mass  of  the  absorbent  material  traversed 
by  the  rays,  and  therefore  is  constant  if  the  density  of  a  vapor  varies  inversely  as  its  depth,  has 
appeared  probable.  To  test  the  assumption  further,  Tyudall  had  two  tubes  whose  lengths  were 
as  3.5  to  1  and  measured  the  percentage  absorptions  of  ether- vapor,  (C2H5)2O,  at  inverse  pressures. 

TABLE  55. 


Radiant  source. 

Inches.               Inches. 
Zi=38.0           _pi-L° 
/:=10.  8           2>2=3.5 

Ip 

38 

Per  cent. 
a=30.  3 
30.0 

A  dull  lime  light 
Brighter  liiue  light 
Brightest  lime  light    . 

38.0 
10.8 

2.0 

7.0 

Ip 

76 

38.8 
38.5 

38.0 
10.8 

1.0 
3.5 

Ip 
38 

22.3 
22.5 

38.0 
10.8 

2.0 
7.0 

If 

76 

29.5 
30.0 

38.0 
10.8 

1.0 
3.5 

Ip 

38 

18.4 
18.8 

38.0 
10.8 

2.0             Ip 
7.0             76 

25.7 
25.6 

The  assumption  of  constant  absorption  of  radiation  from  a  source  of  constant  temperature  by 
an  absorbent  of  constant  mass  is  verified  in  this  case,  the  physical  state  remaining  unchanged. 

The  question  whether  the  absorption  of  a  given  mass  of  material  will  remain  constant  when  its 
state  changes  from  the  liquid  to  the  vaporous  condition  demands  separate  treatment.  Tyndall's 
answer  for  ethyl  ether  is  contained  in  the  following  paired  values : 


Radiant  source. 


Lime  light  with  mirror 


Absorption. 
Per  cent. 

/Ether  vapor     32.  4 


rock-salt  lens 


Incandescent  platinum  with  rock-salt  lens  -I 
The  same  011  another  occasion 


liquid    32. 9 

vapor    33. 3 
liquid    33. 3 

vapor     66. 7 
liquid     67. 2 

vapor     71. 0 
liquid    70. 0 

In  like  manner  hydride  of  amyl  (source  of  radiation  not  stated)  gave  equal  absorptions  of  51 
per  cent,  in  the  two  states.  It  is,  of  course,  impossible  to  assert  from  these  few  observations  that 
alike  identity  of  liquid  and  vaporous  absorption  will  hold  good  for  other  substances,  although 
Tyndall's  opinion  was  to  the  contrary,*  and  I  shall  show  later  that  it  does  not  hold  true  for  water. 

The  experiments  which  give  the  title  to  the  paper  and  introduce  a  novel  method  follow.  By 
interrupting  a  convergent  beam  concentrated  on  a  small  bulb  containing  a  vapor,  employing  for 
this  purpose  a  toothed  wheel  revolved  with  such  rapidity  as  to  give  the  number  of  pulsations 
which  evoked  the  resonance  of  the  bulb,  Tyndall  found  that  the  heat,  instantaneously  absorbed 
and  radiated  by  the  vapor,  produced  alternate  expansion  and  contraction,  giving  a  musical  note 
whose  intensity  was  proportioned  to  the  combined  absorbent  and  radiative  power,  as  well  as  to 
the  difficulty  with  which  the  substance  volatilizes.  The  expansion  could  also  be  made  evident 
upon  a  manometer.  When  radiation  from  a  lime  light  was  concentrated  by  a  mirror  upon  a  cylin- 

*In  regard  to  the  equality  of  liquid  and  vaporous  absorption  Tyndall  says  (p.  500) :  "A  general  law  of  molecular 
pnysics  is,  I  apprehend,  here  illustrated." 


90 

drical  vessel  4  inches  long  and  3  inches  wide,  with  rock-salt  end  plates,  the  following  water 
pressures  were  obtained  on  the  manometer,  according  to  the  contents  of  the  vessel: 


Chloroform,  CH3C1 350  j   Carbon  monoxide,;CO 116 

Aldehyde,  C:H.,O 325      Oxygen,  O, 5 


Olefiant  gas,  CiH4 315 

Ethyl  ether,  (C2H5):O 300 

Nitrous  oxide,  N,O 198 

Marsh  gas,  CH., 161 

Carbon  dioxide,  CO2 144 


Hydrogen,  11? 5 

Nitrogen,  N2 5 

Dry  air 5 

Humid  air,  at  50°  C .130 


Although  a  few  of  the  more  absorbent  of  these  substances,  such  as  nitrous  oxide  and  marsh 
gas,  may  exist  as  barely  perceptible  traces  in  the  Earth's  atmosphere,  and  carbon  dioxide  in  larger 
proportion,  the  interest  of  this  series  to  the  meteorologist  of  course  centers  in  the  absorption  of 
moist  air  relatively  to  that  of  dry  air.  The  numbers,  however,  do  not  coincide  with  the  relative 
absorbent  values,  being  modified  by  the  radiant  powers  of  the  substances,  but  as  it  is  precisely 
this  combination  of  radiative  and  absorbent  qualities  which  determines  the  thermal  state  of  the 
atmosphere,  these  relations  are  significant.  In  alluding  to  their  meteorological  bearing  Professor 
Tyndall  remarks  (p.  516) : 

The  radiant  power  of  air  being  practically  -nil,  it  retains  for  a  considerable  time  the  warmth  imparted  to  it 
during  the  day,  while  when  it  is  dry  the  rays  from  the  surface  of  the  earth  pass  unimpeded  through  it.  Hence  the 
relative  refrigeration  of  the  surface  [at  night  and  in  dry  weather]. 

The  radiant  power  of  dry  air  is  underrated  by  Tyndall  here  and  elsewhere,*  but  the  general 
accuracy  of  his  analysis  of  the  atmospheric  thermal  mechanism  remains  unimpaired. 

If  the  exact  equivalence  in  absorption  by  equal  masses  of  a  substance  in  the  liquid  and  in  the 
vaporous  states  had  been  as  firmly  established  as  Tyndall  imagined,  his  measures  of  the  absorption 
of  liquid  water  (Heat  as  a  Mode  of  Motion,  p.  430)  could  be  utilized  in  connection  with  the  atmos- 
pheric problem.  The  observations,  which  were  made  on  radiation  from  a  plautinum  spiral  raised 
to  a  bright  red  heat  by  an  electric  current,  follow: 

TABLE  56. 


Thickness  of  liquid 
water. 

Absorp- 
tion. 

Inches. 

cm. 

Per  cent. 

0.02 

0.05 

80.7 

0.04 

0.10 

86.1 

0.07 

0.  18 

88.8 

0.14 

0.  36 

91.0 

0.27 

0.69 

91.0 

For  comparison  of  absorption  by  water  in  the  vaporous  condition,  the  following  values  of  the 
absorption  by  an  air  column,  nearly  100  meters  long,  with  varying  humidity,  have  been  taken  from 
a  treatise  on  the  Moon's  radiation,  which  includes  some  subsidiary  researches  on  atmospheric 
absorption  ("The  Temperature  of  the  Moon,  from  researches  made  at  the  Allegheny  Observatory," 
by  S.  P.  Langley,  assisted  by  F.  W.  Very.  National  Acad.  of  Sci.,  vol.  4,  part  2, 3d  Memoir,  p.  186, 
Washington,  1889).  In  the  last  column  I  have  deducted  2.5  per  cent,  from  the  original  numbers  for 
the  absorption  of  carbon  dioxide. 

*  The  small  expansions  of  dry  air  and  its  chief  constituents,  nitrogen  and  oxygen,  are  attributed  by  Tyndall  to 
a  warming  of  the  apparatus  and  to  expansion  of  the  gas  by  heat  communicated  to  it  by  convection,  rather  than  to 
heating  by  direct  absorption  of  radiation  by  the  gas;  but,  as  in  the  case  of  dynamic  heating,  no  sufficient  reason  is 
given  for  rejecting  these  smallest  readings. 


91 

TABLE  57. 


Relative 
humidity. 


Per  cent. 
53 
60 

61.5 
82 


Equivalent 
depth  of 
liquid 
water. 

Absorp- 
tion. 

em. 

Per  cent. 

0.096 

12.1 

.     0.  151 

19.3 

0.166 

21.8 

0.205 

30.4 

Plotting  tlie  observations  with  depths  of  precipitable  water  for  abscissa?  and  absorptions  for 
ordinates,  it  will  be  seen  that  the  curve  (fig.  13)  departs  slightly  from  a  straight  line,  and  more  as 


7 


30 
28 
26 

24 
22 

20 
1* 

16 

12 


X 


-a 


KK 


y 


X 


X 


/ 


•fib 


.53 


10 
8 
6 


0 


aos 


0.15 


0.20  c-m. 


.  13 


the  relative  humidity  increases,  at  least  for  relative  humidities  above  60  per  cent.     I  infer  that  for 
an  equivalent  depth  of  0.2  em.  of  liquid  water,  for  which  an  absorption  of  28.8  per  cent,  is  indicated, 


92 


a  reduction  of  3.6  per  cent,  should  be  made  to  allow  for  au  iucremeut  of  absorption  dependent  upon 
greater  relative  humidity,  the  remaining  absorption  of  25.2  per  cent,  being  due  to  normal  water- 
vapor,  plus  an  unknown  but  evidently  very  small  correction  for  the  effect  of  dry  air. 

For  the  equivalent  depth  of  0.18  cm.  the  absorption  of  water- vapor  is  22.6  per  cent.,  which  may 
be  compared  with  Tyudall's  third  observation  (Table  56),  whence  it  appears  that  for  this  amount 
of  water  the  liquid  absorption  is  four  times  the  vaporous;  but  the  rate  of  absorptive  increase 
with  growing  depth  is  very  different  for  the  two  states,  and  for  an  equivalent  depth  of  one-half 
millimeter  we  have  vaporous  aqueous  absorption,  G.2  per  cent. ;  liquid  aqueous  absorption,  80.7 
per  cent.,  the  liquid  absorption  being  thirteen  times  greater  than  the  vaporous. 

No  allowance  is  made  here  for  any  change  produced  by  differences  in  the  radiant  source;  but 
I  shall  now  develop  a  method  by  which  we  may  be  independent  of  the  temperature  of  the  source. 
By  combining  spectral  energy-curves  and  curves  of  absorption  for  homogeneous  rays,  we  may 
deduce  the  total  absorption  for  any  case  which  can  be  given. 

The  following  measurements  of  the  distribution  of  energy  in  the  spectrum  of  a  blackened 
radiator  filled  with  boiling  water,  and  at  a  distance  of  110  meters,  are  taken  from  page  186  of  the 
memoir  on  the  temperature  of  the  Moon,  already  cited.  The  barometer  stood  at  739  mm.,  and  the 
mean  dew-point  was  +  12°.7  C.,  corresponding  to  0.122  cm.  of  precipitable  water.  The  deviations 
are  those  of  a  rock-salt  prism  whose  angle  (p.  132  loc.  cit.)  was  ''always  very  near  60°."  The  trans- 
formation factor,  for  reducing  the  galvanometer  deflections  to  those  of  a  normal  spectrum, 
are  taken  from  my  paper  "Further  considerations  in  regard  to  laws  of  radiation"  (Astrophysical 
Journ.,  vol.  4,  p.  43,  June,  1896),  and  the  wave-lengths  are  from  Eubens'  dispersion  curve  adopted 
in  the  same  paper. 

TABLE  58. — Spectral  energy-curves  through  water-vapor  (radiant  source,  99°  C.). 


Minimum 
deviation 
(rock-salt.) 

Wave- 
length. 

Prismatic 
deflection. 

Transforma- 
tion factor. 

Xormal 
deflection. 

o 

U 

OQ  1 
Oi/4 

3.10 

31.3 

.305 

9.5 

39 

4.26 

40.0 

.364 

14.6 

38| 

5.22 

48.8 

.432 

21.1 

38* 

6.03 

28.4 

.491 

13.9 

38i 

6.76 

30.2 

.549 

16.6 

38 

7.41 

42.6 

.599 

25.5 

37f 

8.01 

52.0 

.647 

33.6 

37| 

8.59 

55.7 

.691 

38.5 

37i 

9.11 

62.0 

.733 

45.4 

37 

9.60 

50.0 

.772 

38.6 

36i- 

10.45 

48.0 

.839 

40.3 

36' 

11.2 

42.0 

.898 

37.7 

35| 

11.85 

33.2 

.  949           31.  5 

35 

12.4 

27.2 

.  991           27.  0 

Eadiations  of  shorter  wave-length  than  about  2/t  are  inappreciable  in  the  spectrum  of  a 
body  at  the  boiling  point  compared  with  one  at  the  freezing  point  of  water,  and  I  have  omitted 
such,  assuming  them  to  have  been  due  either  to  reflected  solar  rays  or  to  errors  of  observation. 
As  the  aperture  for  admitting  radiation  from  the  distant  radiator,  whose  area  was  over  1  sq.  m., 
also  permitted  wind  to  blow  upon  the  measuring  instruments,  some  irregularities  are  due  to  this 
cause ;  but  the  great  depression  between  5/i  and  9//,  in  fig.  14,  where  the  normal  ordinates  in  the 
last  column  of  Table  58  are  plotted,  occupies  the  position  of  the  great  absorption-baud  of  aqueous 
vapor  and  must  be  attributed  to  it. 

Table  59  contains  a  spectral  energy-curve  observed  with  a  fluorite  prism  by  Paschen  through 
33  cm.  of  aqueous  vapor  at  100°  0.,  corresponding  to  a  layer  of  0.0194  cm.  of  precipitable  water. 
(Wied.  Ann.,  Bd.  51,  Taf.  1,  fig.  3,  heft  1, 1894.) 


93 

TABLE  59. — Absorption  by  steam. 


Minimum 
deviation 
(fluorite). 

"Wave- 
length. 

Radiation 
nuabsorbed. 

Radiation 
after 
absorption. 

Transmis- 
sion. 

Absorption. 

O              ' 

ft 

Per  cent. 

Per  cent. 

28    46.5 

5 

99                 74 

74.7 

25.3 

28     16 

5.5 

76 

16 

21.1 

78.9 

i'T    41.  r, 

6 

56     . 

5 

9.0 

91.0 

27      5.5 

6.5 

41 

3 

7.3 

92.7 

26    25.  5 

.     7 

30.5 

6 

19.7 

80.3 

25    40 

7.5 

21 

15 

71.4 

28.6 

24    52 

8 

14.5 

13.5 

93.1 

6.9 

24       1 

8.5 

7.5 

7.5 

100 

0 

The  measured  radiations  are  not  given  in  this  paper,  and  the  values,  corresponding  to  ether- 
waves  differing  in  length  by  half  a  micron,  have  been  read  from  the  curves.  The  source  of  radia- 
tion was  a  hot  sheet-iron  cylinder  over  an  Argaud  burner.  The  absorbent  vapor  was  contained 
in  a  cylindrical  metal  tube  4  or  5  cm.  in  diameter,  closed  by  end  plates  of  thinnest  copper,  in 
which  were  open  slits  "of  such  dimensions  that  no  rays  reflected  from  the  inner  walls  of  the  tube 
could  reach  the  bolometer,  but  only  such  radiation  as  had  passed  directly  through  the  gas  layer 
in  the  tube.  In  this  way  all  disturbance  by  '  adhesion  of  vapor,'  etc.,  was  excluded.  A  slender 


20 


10 


\ 


01      234-56      7     S      9     10     11     12     13 


15    16    17    ft     /9    20   21 M 


Great   water-vapor   absorption-band.     (Equivalent    liquid  =  0.122    cm.}.     Energy-curve  of  normal 
spectrum,  reduced  from  rock-salt  prismatic  spectrum. 

metal  tube  was  screwed  into  the  middle  of  the  tube.  This  served  to  convey  the  gas  under  inves- 
tigation in  a  slow  but  steady  stream  through  the  tube.  In  this  way  there  was  interposed  a 
flowing  layer  of  gas,  of  dimensions  not  exactly  known,  but  very  constant."  (Loc.  clt.,  p.  4.)  These 
measures  are  not  available  to  as  great  wave-lengths  as  those  made  with  a  rock-salt  prism,  because 


94 


the  absorption  of  fluorite  nearly  obliterates  the  radiation  in  the  extreme  infra-red  spectrum  where 
water- vapor  begins  to  recover  trausmissive  power. 

Completing  the  missing  portion  of  the  energy-curve  in  fig.  14,  as  in  the  upper  broken  line,  by 
the  aid  of  spectral  measures  on  a  near  radiator  at  the  same  temperature  in  dry  weather,  and 
adjusting  the  areas  so  as  to  give  the  same  absorption  (15.3  per  cent.)  which  the  curve  in  fig.  13 
indicates  for  a  depth  of  0.122  cm.  of  precipitable  water,  the  following  radiant  energies  and 
percentages  of  absorption  are  obtained: 

TABLE  60. — Absorption  by  aqueous  vapor. 


Wavi- 

Kmliatinn           Kwliatioii          Pei.cent!is,, 

Absorption. 

length. 

on  absorbed. 

absorption. 

traiKsimtreu. 
0.1220  cm.* 

0.0194  cm.t 

0.0041  cm.  J 

M 

Per  cent. 

Per  cent. 

Per  cent. 

5                        26.0 

21.3 

81.9 

18.1 

25.3 

5 

5.5                    31.2 

19.0 

60.9 

39.1 

78.9 

40 

6                        36.4 

14.0  i              38.5 

61.5 

91.0 

68 

6.5 

41.6 

14.  0                33.  7 

66.3 

92.7 

70 

7 

45.6 

20.0 

43.9 

56.1 

80.3 

47 

7.5 

48.0 

26.8 

55.8 

44.2 

28.6 

20 

8 

48.5 

32.2 

66.4 

33.6 

7.9 

14 

8.5 

47.6 

39.  2                82.  4 

17.6 

0 

5(f) 

*  Absorption  by  water  vapor  in  110  meters  of  air  at  ordinary  summer  temperature,  equivalent  to  0.1220  cm.  of  liquid  water, 
t  Absorption  by  33  cm.  of  steam  at  100°  C.,  equivalent  to  0.0194  cm.  of  liquid  water.     (Paschen,  Wied.  Ann.,  as  above,  Table  59.) 
t  Absorption  by  7  cm.  of  steam  at  100°  C.,  equivalent  to  0.0041  cm.  of  liquid  water.     (Paschen,  Wied.  Ann.,  Bd.  52,  Taf.  II,  fig.  1,  curve 
1  c,  in  which,  ordinates  are  percentages  of  absorption.) 

For  comparison  two  series  of  absorption  values  for  steam,  deduced  from  curves  given  by 
Professor  Paschen,  are  included  in  the  last  two  columns  of  Table  GO.  These  are  not  obtained 
by  direct  measurement,  but  from  a  comparison  of  the  curve  of  observation  after  absorption  with  a 
restoration  by  estimation  of  the  curve  before  absorption.  In  regard  to  the  restoration,  obtained 
by  drawing  a  continuous  curve  tangent  to  the  shoulders  on  either  side  of  the  band,  Paschen  says 
(Wied.  Ann.,  Bd.  51,  S.  11)  that  it  "has  thus  too  low  rather  than  too  high  ordinates,"  and  in 
consequence  the  indicated  absorption  is  too  small.  This  especially  affects  the  estimates  of 
absorption  of  the  longer  waves  from  7.5  //  to  9  //,  where,  the  energy  being  very  small  in  the  fluorite 
spectrum,  a  comparatively  slight  change  in  the  curve  will  produce  a  large  alteration  in  the 
estimated  absorption.  The  effect  of  this  error  is  less  noticeable  with  a  source  of  radiation  at  a 
high  temperature,  such  as  was  used  by  Paschen,  but  applied  to  observations  on  a  low-temperature 
source,  these  small  absorption  values  from  7.5  ;.i  to  9  //  will  give  a  restored  curve  of  uuabsorbed 
radiation  having  a  depression  at  the  maximum,  which  is  inadmissible.  The  larger  values  of 
absorption  are  therefore  to  be  preferred  at  the  borders  of  the  band,  at  least  on  the  side  of  greater 
wave-length. 

A  further  comparison  of  these  results  shows  that  a  short  column  of  concentrated,  or  satu- 
rated vapor  absorbs  more  powerfully  than  an  equal  amount  largely  diluted  with  air,  and  further 
from  the  point  of  saturation.  The  absorption  of  a  layer  of  saturated  steam,  7  cm.  deep  (Table  00, 
Series  3)  containing  0.0041  cm.  of  precipitable  water,  undiluted,  exercises  as  great  an  absorption 
as  0.1220  cm.  of  precipitable  water  distributed  as  uusaturated  vapor  through  11,000  cm.  of  air. 
The  quantity  of  vapor  is  here  30  times  as  great,  the  dilution  1,571  times  as  great  in  case  1  (Table 
CO)  as  in  case  3.  I  have  shown,  however,  that  in  the  free  air,  where  the  dilutions  are  not  widely 
different,  the  absorption  is  nearly  proportional  to  the  vapor  contents,  at  least  up  to  a  depth  of 
100  meters. 

A  more  extensive  comparison  may  be  made.  I  have  found  that  a  layer  of  water,  40  cm.  thick, 
is  almost  absolutely  impervious  to  solar  infra-red  radiation  beyond  wave-length  1.0  p.  No  such 
absorption  occurs  with  the  most  humid  air  as  the  sun  approaches  the  horizon,  although  the  abso- 
lute amount  of  water  in  a  vaporous  form,  interposed  in  the  path  of  the  rays,  must  often  be  even 
greater  than  that  contained  in  a  liquid  layer  40  cm.  thick.  Hence  from  the  result  of  this  test, 
made  for  us  in  nature  on  a  grand  scale,  we  have  conclusive  evidence  that  the  selective  absorption 
of  vaporous  water  is  not  identical  with  that  of  liquid  water,  but  that  the  former  is  comparatively 


95 


permeable  to  infra-red  radiations.  Nevertheless,  the  general  form  of  the  absorption  curve  in  the 
infra-red  spectrum,  as  to  its  coarsest  details,  or  broad  groups  of  absorption-bands,  and  their  rela- 
tive intensities  is  very  similar  in  the  two  cases. 

Passing  to  the  absorption- spectrum  of  liquid  water,  I  have  measured  the  ordiuates  in  the 
spectral  energy-curves  for  a  fluorite  prism  which  Pascheu  has  given  ( Wied  Ann.,  Bd.  52,  1894, 
Taf.  II,  fig.  2,  curves  1  to  4),  in  which  a  blackened  platinum  strip  at  450°  C.*  was  the  radiant 
source.  These  readings  have  been  divided  by  the  ordinates  with  empty  cell  to  obtain  the  corre- 
sponding percentage  transmissions  which  are  given  in  the  next  table. 

TABLE  61. — Absorption  by  liquid  water. 


Wave-length. 

2fi          2.5/x 

3* 

3.5M 

4  n-i          4.  5  ju.          5  ju.          5.  5  /LI          6/A          6.5/x 

7.          7.5M          8^          8.5^ 

Min.  deviation  .  . 

30°  47'     30°  34' 

30°  18' 

29°  59' 

29°  38'     29°  14'  !  28°  47'     28°16'     27°42'      27°6' 

26°  26' 

25°  40' 

24°  52' 

24°!' 

WATER. 

cm. 

0.0000           374           507 

007 

556 

443 

339           262           194 

133 

101 

86 

63 

38 

18 

a 

v 

-S 

0.  0015           350 

373 

58 

397 

318 

244           193           146 

45 

64 

60            42 

28 

16 

2 

0.  0030 

340 

330 

6 

317 

298           135           135             92 

5 

15 

18             14 

9 

6 

H 

0.  0080 

305 

135 

2 

137 

147             21             33             23 

2 

•  a 

.0015 

93.6         73.6 

9.6 

71.4 

71.8 

72.  0         73.  7         75.  3 

33.8 

63.4 

69.8         66.7 

73.7 

88.9 

If 

.0030 

90.  9         65.  1 

1.0 

57.0 

67.3 

39.8         51.5         47.4 

3.8 

14.9         20.9 

22.2 

23.7 

33.3 

H'S 

.0080 

81.6 

26.6 

0.3 

24.6 

33.2 

6.2         12.6         11.9 

1.5 

. 

& 

.0015 

6.4 

26.4 

90.4 

28.6 

28.2 

28.0         26.3         24.7         66.2 

36.6 

30.2 

33.3 

26.3 

11.1 

'5  ^ 

.  0030           9.  1 

34.9 

99.0 

43.0 

32.7 

60.2         48.5         52.6         96.2 

85.1 

79.1 

77.8 

76.3 

66.7 

—  ^ 

^ 

.  0080         18.  4 

73.4 

99.7 

75.4 

66.8 

93.8         87.4         88.1         98.5 

The  transmissions  in  this  table,  for  the  longer  wave-lengths,  have  been  multiplied  by  the 
ordinates  of  an  uuabsorbed  normal  spectral  energy-curve  at  100°  0.  to  obtain  the  figures  in  the 
last  three  lines  of  Table  62,  and  the  curves  in  fig.  15. 

TABLE  62. — Spectral  energy-curves  through  liquid  water  (radiant  source  100°  C.). 


Wave-length. 

5p 

5.5/a 

BM 

6.5/ii 

7/u 

7.5ft.                  Sfj. 

8.5M 

WATER. 

cm. 

(1)     0.  0000 

26.0 

31.2 

36.4 

41.6 

45.6 

48.0 

48.5 

47.6 

(2)    0.0015 

19.2 

23.5 

12.3 

26.4 

31.8 

32.0             35.7 

42.3 

(3)    0.0030 

13.4 

14.8 

1.4 

6.2 

9.5 

10.  7             11.  5 

15.2 

(4)     0.  0080 

3.3 

3.7 

0.5 

[0.5] 

[2.2] 

[2.8] 

[1.0] 

[2.0] 

Measures  made  with  a  fluorite  prism  are  not  available  for  wave-lengths  longer  than  9  ju  where 
the  absorption  of  fluorite  becomes  large,  but  after  this  point  aqueous  absorption  is  comparatively 
insignificant  until  the  region  of  the  spectrum  beyond  13  //  is  reached.  Solar  and  lunar  radiations 
longer  than  9  //  penetrate  our  atmosphere  freely,  even  in  moist  summer  weather,  and  Tyndall's 
observations  (quoted  in  Table  56)  show  that  9  per  cent,  of  the  rays  from  platinum  at  a  bright-red 
heat  resist  the  absorption  of  liquid  water.  This  remnant  is  distributed  at  irregular  intervals 
through  the  spectrum.  As  the  region  beyond  12.5  //.comprises  but  a  small  fraction  of  the  total 
energy  from  such  a  source,  I  shall  assume,  merely  for  the  present  purpose,  that  aqueous  absorp- 
tion ends  at  12.5  //,  and  as  it  is  probable  that  certain  feeble  atmospheric  absorption  bands  of 

*Subsequeut  measures  by  Paschen  have  indicated  that  the  uuabsorbed  maximum  in  this  curve  has  been  dis- 
placed toward  the  shorter  wave-lengths,  owing  to  the  imperfect  absorption  of  the  loug  waves  by  the  bolometer, 
and  that  the  maximum  should  be  at  4  //. 


96 


greater  wave-length  than  9  /*  are  due  to  water-vapor,  the  curves  are  drawn  undulating  in  the 
dotted  portions  supplied  to  complete  the  areas.  The  spectral  region  between  9  //  and  12  jj.  is  very 
readily  transmitted  by  water- vapor,  but  the  limits  of  liquid  absorption  are  wider.  Aqueous 


0/2345 


7      8      9     10     11     12     13    14    15    16    il    18     f9    20    21  JU 


ffig.    15 


Energy-curves  of  normal  spectrum  after  absorption  by  liquid  water. 

absorption  increases  again  gradually  beyond  12  //,  and  is  perhaps  the  cause  of  the  practical 
ending  of  the  spectrum  near  20  /;. 

Measuring  the  areas  of  the  curves  in  fig.  15,  and  comparing  2,  3,  and  4  successively  with  the 
unabsorbed  energy-curve  (1),  the  following  transmissions  of  total  radiation  from  a  source  at 
100°  C.  are  obtained : 

TABLE  (53. 


Depth  of  liquid 

Area  of  spectral 

Transmission  of 

Absorption  of 

water. 

energy  curve. 

total  radiation. 

total  radiation. 

cm. 

Per  cent. 

Per  cent. 

(1)     0.0000 

1.420 

100.0 

0 

(2)     0.0015 

1.016 

71.5 

28.5 

(3)     0.0030 

0.630 

44.4 

55.6 

(4)     0.0080 

0.341 

24.0 

76.0 

If  the  aqueous  absorption  is  exercised  on  radiation  from  a  red-hot  source,  wave-lengths  from 
2ju  to  5/i  must  be  included,  which  is  done  in  Table  04,  the  transmissions  being  obtained  from 
Table  61,  and  combined  with  radiant  values  from  a  normal  spectral  energy-curve,  taken  from  the 
reduction  for  a  source  estimated  at  815°  C.,  given  in  rny  paper,  u  Further  considerations  concerning 
laws  of  radiation"  (Astropliysical  Joitrn.,  vol.  4,  p.  43),  in  which,  however,  the  temperature  has 
probably  been  placed  too  high,  since  the  position  of  the  unabsorbed  maximum  more  nearly  agrees 
with  that  of  the  ideal  black  body  at  450°  C.  (see  footnote,  p.  95 5  compare  also  my  note  in  Astroph. 
Journ.,  vol.  10,  p.  208,  Oct.,  1899) ;  but  the  discrepancy  may  arise  in  part  from  the  use  in  the 
present  case  of  a  radiant  which  is  not  an  ideal  black  body. 


97 


TABLE  04. — /Spectral  energy -curves  through  liquid  water  (radiant  source  815°  C.  ?). 


Wave-length.          In          2.5ft.         3|u 

3.5.           4, 

8ju. 

9, 

lOju 

15,     ;     20, 

WA.TKB. 

em. 

(1)     0.0000 

40 

67       160       187       193 

190        isi' 

154       117         84 

60 

42 

16 

o 

(2)     0.0015 

37.4 

49.  3     15.  4 

133.5   138.6 

136.8    134.1 

52.1     81.7     61.9 

(3)     0.  0030 

36.4 

43.6       1.6 

106.6   129.9 

75.6 

93.7 

5.  9     24.  5     19.  9 

(4)     0.0080 

32.6 

17.8       0.5 

46.  0     64.  3 

11.8 

22.9 

2.3 

• 

These  values  are  plotted  in  fig.  16.  Three  principal  regions  of  large  absorption  are  shown. 
The  first,  extending  from  2.2/i  to  3.7^u,  with  the  minimum  near  3//,  occupies  the  position  of  Lang- 
ley's  X  and  associated  bands  (xi  Xi)  in  ^ne  solar  spectrum.  The  second  depression  from  4.2//  to 
5.2/<  (minimum  at  4.7/0  encroaches  on  the  great  carbon  dioxide  baud,  but  does  not  seem  to  be  as 


^oo 


150 


\ 


\ 


\ 


oLZ 


0     /      2     3     4     5     6     7      8 


to    ft    12    f3    14    i5    16    11 
l.     16 


f<J    20  2i 


Energy-curve*  of  normal  spectrum  after  absorption  by  liquid  water. 

strongly  developed  in  the  vaporous  absorption  of  water:  neither  does  it  appear  in  the  absorption 
of  0.0015  cm.  of  liquid  water,  although  quite  well  marked  in  the  curve  for  0.0030  cm.  The  third 
region  is  that  of  the  great  aqueous  absorption  band  from  5.2  jn  to  7.0/<  with  a  subordinate  extension 
to  9//,  its  deepest  depression  being  at  6.  1//.  The  vaporous  absorption  differs  in  showing  two 
minima,  at  5.86/<  and  6.51/<.  A  succession  of  smaller  bands  follows,  the  absorption  of  the  liquid 
diminishing  from  S^u  to  12/».  In  this  region  aqueous  vapor  has  very  free  transmission,  and  the 
same  is  true  of  a  liquid  layer  0.0015  cm.  thick. 
12812—  Bull.  G  -  7 


98 


Comparing  areas  in  fig.  16  the  following  transmissions  of  total  radiation  from  a  source 
estimated  at  815°  C.  are  found : 

TABLE  65. 


.    Deptli  of  liquid 
water. 

Area  of  spectral 
energy  curve. 

Transmission  of 
total  radiation. 

Absorption  of 
total  radiation. 

cm. 

Per  cent.                 Per  cent. 

(1)         0.0000 

2.576 

100 

0 

(2)         0.  0015 

2.175 

84.4 

15.6 

(3)         0.0030 

1.487 

57.7 

42.3 

(4)         0.  0080 

1.015 

39.4 

60.6 

Within  the  given  limits  of  temperature  (100°  and  815°  C.)  the  transmission  for  every  thickness 
is  greatest  for  the  radiation  from  the  hotter  source,  a  result  which  is  as  old  as  the  measurements  of 
Melloni,  but  which  is  here  presented  no  longer  as  an  empirical  fact,  but  as  a  piece  of  knowledge 
which  may  be  rationally  conceived  and  which  can  be  applied  deductively  to  a  variety  of  special 
cases. 

We  are  now  in  a  position  to  assert  confidently  that  so  long  as  the  physical  state  remains 
unchanged  and  the  total  aqueous  absorption  does  not  exceed  50  per  cent,  the  increment  of  aqueous 


cm 


absorption  is  nearly  proportional  to  the  depth  of  the  absorbing  layer,  but  beyond  this  point  the 
rate  of  increase  in  the  absorption  falls  off  very  rapidly  until  finally  further  addition  to  the  layer 
produces  almost  no  effect. 

Next,  by  comparing  the  curves  in  figs.  13  and  17,  it  can  be  stated  that  the  absorption  of  total 


99 


radiation  by  water-vapor  iu  bigb  dilution  in  the  free  air  falls  far  below  its  absorption  when 
condensed  to  the  liquid  state,  but  in  a  ratio  which  varies  with  the  depth  of  the  absorbent  mass, 
as  the  following  table  shows: 

TABLE  66. — Aqueous  absorption  of  total  radiation  (radiating  body  at  100°). 


Depth  of  pre-      Absorption       Absorption 
cipitable            by  liquid            bv  vapor 

Ratio 
liquid  absorp" 

water.                water. 

in  100  m.  air. 

vapor  absorp". 

cm. 

Per  cent. 

.001 

19.5 

0.125 

156 

.002 

38.0 

0.250 

152 

.003 

55.5 

0.375 

148 

.004 

63.  3 

0.500    1              127 

.005 

67.9 

0.  625                  109 

.006 

71.2 

0.750 

95 

.007 

73.8 

0.875 

84 

.008 

76.0 

1.000 

76 

.009 

78.0 

1.125 

69 

.010 

79.8 

1.250 

64 

From  this  comparison  it  appears  that  with  a  radiating  source  at  the  boiling  point  of  water, 
10  microns  of  liquid  water  absorb  156  times  as  powerfully  as  the  same  amount  of  water  dis- 
tributed in  the  vaporous  state  through  about  100  meters  of  air.  We  have  seen  that  even  an 
approach  of  the  aqueous  vapor  to  its  condensation  point  increases  its  absorptive  power  (Table  57 
and  fig.  13).  Paschen's  result,  already  described  (ante,  p.  94),  shows  that  saturated  aqueous 
vapor  at  100°  C.  exercises  an  intermediate  absorption  between  that  of  the  liquid  and  the  invisible 
nonsaturated  vapor  of  the  atmosphere,  40  microns  of  liquid  water  absorbing  63  per  cent,  of  radia- 
tion from  a  source  at  100°  C.  (by  Table  66),  while  the  same  quantity  of  water  in  the  form  of  steam 
takes  out  about  15  per  cent.,  and  distributed  as  atmospheric  vapor  only  one-half  of  1  per  cent,  (by 
fig.  13  and  Table  66). 

The  identity  of  absorption  in  the  liquid  and  vaporous  states  which  Tyndall  found  for  ethyl 
ether  and  amyl  hydride,  presumably  obtains  only  for  those  substances  which  do  not  change  their 
molecular  constitution  in  passing  from  one  state  to  the  other.  The  influence  of  molecular  form 
upon  absorption  was,  indeed,  recognized  by  Tyudall,  who  says  ( Contributions  to  Molecular  Phys., 
p.  98): 

No  coincidence  between  the  vibrations  of  a  radiating  body  and  those  of  oxygen,  hydrogen,  or  air  could  make  any 
one  of  these  substances  a  good  absorber.  They  are  physically  incapacitated  from  communicating^  motion,  and  hence 
in  an  equal  degree  from  accepting  motion.  The  form  of  the  atom  [molecule?!,  therefore,  or  some  other  attribute 
than  its  period  of  oscillation  [let  us  say,  rather,  some  attribute  on  which  that  period  depends],  must  enter  into  the 
question  of  absorption. 

See  also  pages  102-105  (loc.  cit.),  where  ozone  is  shown  to  absorb  immensely  more  than  oxygen. 
The  atoms  are  here  the  same.  It  is  the  molecular  form  alone  which  has  changed. 

It  is  probable  that  some  of  the  most  important  selective  radiations  of  these  elementary  gases 
are  of  short  wave-length  and  are  not  emitted  until  high  temperatures  are  reached.  We  know  that 
the  linear  absorption  of  cold  oxygen  in  the  visible  spectrum  is  very  feeble,  requiring  a  long 
column  of  gas  to  show  the  A,  B,  and  a  groups  of  lines  in  the  spectrum  of  a  lime-light;  but  there 
is  a  region  of  great  absorption  in  the  extreme  ultra-violet.  Von  Schumann  finds  that  a  layer  of 
air  linni.  thick  cuts  off  all  rays  beyond  0.175//;  and  Liveing  and  Dewar  (Proc.  E.  Soc.  London,  vol. 
46,  p.  222,  1889)  have  found  that  the  absorption  of  18  meters  of  oxygen  in  the  ultra-violet  is  of  the 
nature  of  a  broad  diffuse  band,  whose  limits  extend  to  greater  wave  lengths  on  the  less 
refrangible  side  as  the  pressure  increases.  At  a  pressure  of  97  atmospheres,  when  the  mass  of 
oxygen  in  their  tube  was  "rather  greater  than  is  contained  in  a  vertical  column  of  equal  section 
of  the  Earth's  atmosphere,"  the  rays  were  completely  absorbed  to  a  wave-length  of  0.2797//.  At 
50  atmospheres  the  total  absorption  had  its  limit  at  0.2696^;  and  at  23  atmospheres  the  limit  of 
extinction  had  receded  to  0.2599//. 

Two  kinds  of  bands  appear  in  the  absorption-spectrum  of  oxygen,  in  regard  to  which 


100 

Professors  Liveing  and  Dewar  make  some  suggestions  which  are  of  interest  in  the  present  con- 
nection : 

The  absorptions  of  the  class  to  which  A  and  B  belong  must  be  those  \\hich  are  most  easily  assumed  by  the 
diatomic  molecules  (O2)  of  ordinary  oxygen.  As  for  the  other  class  of  absorption,  the  diffuse  bands,  since 

they  appear  to  have  intensities  proportional  to  the  square  of  the  density  of  the  gas,  they  must  depend  on  a  change 
produced  by  compression.  This  may  either  be  the  formation  of  more  complex  molecules,  as  for  example  O^,  corre- 
sponding to  the  deviation  from  Boyle's  law  exhibited  by  oxygen  gas,  or  it  may  be  the  constraint  to  which  the 
molecules  are  subject  during  their  encounters  with  one  another.  Increase  of  temperature  would  affect  the  former, 
tending  to  diminish  the  number  of  complex  molecules  formed  at  a  given  pressure,  but  would  have  no  effect  on  the 
latter,  for  though  the  number  of  encounters  of  the  molecules  in  a  length  of  time  would  be  greater  the  higher  the 
temperature,  yet  so  long  as  the  volume  was  unaltered  the  ratio  of  the  duration  of  an  encounter  to  that  of  free 
motion  would  be  sensibly  unaltered.  So  far  as  any  change  due  to  temperature  has  been  observed,  it  is  that  a  rise 
of  temperature  slightly  weakens  the  diffuse  absorptions  (loc.  cit.  pp.  227,  228). 

Consequently  these  observations  favor  the  hypothesis  that  compression  produces  a  limited 
number  of  complex  and  highly  absorbent  oxygen  molecules  which,  even  though  few  in  number, 
are  able  to  impress  a  peculiar  character  upon  the  spectrum. 

Profs.  W.  Ramsay  and  J.  Shields  ("The  molecular  complexity  of  liquids,"  Trans.  Journ.  Chem. 
Soc.  London,  vol.  63,  p.  1089,  1893),  from  their  experiments  on  the  surface  tension  of  liquids  as 
a  function  of  the  relative  number  of  molecules  per  square  centimeter  of  surface  and  the  tempera- 
ture, conclude  that  several  molecules  of  water-vapor  unite  to  form  a  complex  molecule  of  liquid 
water;  but  ethyl  oxide  has  the  same  molecule  in  the  liquid  as  in  the  vaporous  state.  Regarding 
oxygen  as  tetravalent,  the  liquid  molecules  of  water  may  be  closed  chains,  e.  g.: 

H     H 

C-U-, 


H— O— O— H 

H— O— O— H 


(H20)4=          I        | 


At  60°  C.  the  composition  of  the  liquid  molecule  of  water  is  (H2O)^,  while  at  the  temperature 
of  maximum  density  most  of  the  complex  molecules  are  represented  by  the  second  formula. 

The  gradual  formation  of  closed  chains  as  the  aqueous  vapor  approaches  saturation,*  must 
take  place  most  readily  if  the  molecules  of  vapor  are  not  widely  separated  by  diluting  air. 
Meteorologists  have  often  commented  on  the  peculiarities  of  nearly  saturated  air,  and  some  have 
conjectured  that  gaseous  water  exercises  no  appreciable  absorption,  and  that  the  absorbent 
effects  attributed  to  it  are  really  due  to  a  mist  of  liquid  water,  relative  humidity  being  more 
important  than  vapor  tension  as  an  index  of  absorptive  power.  We  have  seen  that  gaseous 
water  does  produce  a  very  potent  influence  of  its  own,  but  it  seems  to  me  to  be  demonstrated  by 
what  precedes  that  there  is  a  remarkable  increase  in  absorption  by  water  at  the  critical  point  of 
incipient  condensation,  and  as  this  point  is  somewhat  closely  approached.  The  suffocating  sensa- 
tions experienced  in  a  very  hot  muggy  atmosphere  are  attributable  to  the  partial  cessation  of 
evaporation  from  skin  and  lungs,  but  the  thermometric  effects,  such  as  the  diminution  of  the 
daily  range  of  temperature  under  a  clear  sky,  which  becomes  very  noticeable  when  the  relative 
humidity  is  high,  can  be  due  only  to  strong  absorption  of  the  long-waved  terrestrial  radiations, 
and  it  is  interesting  to  note  that  the  difference  between  the  absorption  of  liquid  and  vaporous 
water  lies  chiefly  in  the  greater  absorption  of  longer  waves  by  the  former.  Professor  Pascheu 
says  (  W ied.  Ann.,  Bd.  51,  S.  22,  1894) : 

Liquid  water  has  a  very  deep  absorption-band  which  reaches  from  [fluorite  minimum  deviation]  29°  55' 
[3.58//J  to  30°  40'  [2.29/<],  and  has  its  maximum  at  30°  23',  2.92u  [subsequently  corrected  to  2.84/<],  while  the  corre- 
sponding band  of  the  water- vapor  at  100°  extends  from  30°  18'  [3.00/<]  to  30°  40'  [2.29//J,  and  has  its  maximum  at 
30°  31',  2.66/i  [subsequently  corrected  to  2.58//].  That  of  the  liquid  water  begins  consequently  at  the  same  place 
as  the  gaseous  on  the  side  of  the  short  waves,  but  ends  at  longer  waves.  A  maximum  also  appears  in  [the  absorp- 
tion of]  liquid  water  at  27°  40'  [6.02//]  ;  for  water-vapor  at  100°  its  position  is  27°  53'  [5.85/*].  *  If  we 
remember  that  the  emission-maximum  of  the  oxyhydrogen  name  lies  at  30°  26'  [2.75/u],  we  can  indeed  say  that 

*  Compare  Regnault's  observations  cited,  ante,  p.  85. 


101 

liquid  water  absorbs  the  vibrations  that  the  gaseous  emits  or  absorbs.  The  liquid  absorbs,  however,  in  addition, 
such  as  belong  to  neighboring  longer  waves,  and  these  indeed  so  much  stronger  that  the  absorption-maximum  lies 
3'  farther  toward  the  long  waves  than  the  emission-maximum  of  the  oxyhydrogen  flame. 

The  spectral  energy-curve  of  the  oxyhydrogen  flame,  given  by  Pascheu  ( Wied.  Ann.,  Bd.  51, 
Taf.  1,  tig.  6,  1894),  shows,  in  addition  to  the  emission-baud  just  mentioned,  which  corresponds 
•with  the  absorption-band  of  the  solar  spectrum  called  A'  by  Langiey,  also  the  correlatives  of  the 
solar  bands  fl  and  W.  The  band  A"  is  partly  due,  and  the  baud  Y  wholly  due,  to  the  absorption- 
bands  of  carbon  dioxide,  discovered  by  Knut  Angstrom.  I  quote  Paschen's  description  of  his 
identifications : 

Since  Langley's  bands  W,  fl,  X,  Y,  etc.,  coincide  within  the  errors  of  measurement  with  the  absorption-bands 
determined  by  me,  we  may  refer  the  given  bands  of  the  solar  spectrum  with  great  probability  to  the  CO2  and  H:O 
contained  in  our  atmosphere.  The  wave-lengths  of  Langley's  bands  are:  W  at  1.4//,  corresponding  to  the  emission- 
band  of  H:O  at  1.4/w ;  £1  at  1.83//,  corresponding  to  an  emission-band  of  H;O  at  1.83// ;  J=2.64yU,  corresponding  to 
H;O  =  2.66/u  ;  Langley's  band  widens  at  low  sun  toward  the  longer  waves.  The  new  band  arising  at  2.94//  coincides 
with  the  absorption-maximum  of  liquid  water  which  I  find  lying  at  2.92/<.  r=4.6//  corresponds  to  the  COa  baud 
at  4.63//.  From  5u  to  ll/«  Laugley's  solar  spectrum  is  divided.  Here  lie  the  strong  water-vapor  absorptions  (maxima 
at  7. 1//  and  8.1/<).  (Loc.  cit.,  p.  18.) 

The  last  two  wave-lengths  were  subsequently  corrected  after  more  accurate  comparison  of 
deviations  from  a  fluorite  prism  and  wave-lengths  as  given  by  a  grating,  becoming  5.86yw  and 
6.51//.  The  limits  of  the  great  water  baud  are  also  more  nearly  S^u  and  8//,  the  correction  affect 
ing  chiefly  the  wave-lengths  above  5  microns.  In  this  passage  Dr.  Pascheu  has  misunderstood 
Laugley's  use  of  the  word  "  maximum,"  which  refers  to  an  elevation  in  the  energy-curve  of  tlie 
solar  spectrum  and  not  to  the  point  of  greatest  absorption  in  a  cold  band.  Langiey  (Am.  J.  Sci. 
(3),  vol.  30,  p.  403,  1888)  distinctly  says  that  2.94/<  is  a  subordinate  maximum  of  the  solar  spectral 
energy-curve,  and  again  he  says  (p.  404):  "From  4.0/<  to4.5//  we  have  another  region  of  almost 
complete  absorption,  followed  by  a  maximum  at  4.6//."  It  appears  probable  that  some  of  these 
numerical  values  will  require  further  slight  adjustment.  Langley's  original  value  for  the  center 
of  Y,  namely,  4.25;/,  has  since  been  confirmed  by  Paschen,  who  gives  from  his  measures  with  a 
grating  4.245;<  ( Wied.  Ann.,  Bd.  52,  S.  222). 

The  region  of  the  solar  spectrum  from  wave-length  2.3//  to  3.3/<  is  especially  variable. 
Subordinate  absorption-bauds  on  the  less  refrangible  side  of  A  become  apparently  transposed  in 
relative  importance  as  the  altitude  of  the  sun  above  the  horizon  or  the  vapor-contents  of  the 
atmosphere  change. 

Observations  made  during  the  winter  indicate  that  the  baud  at  2.64,/u  is,  with  a  high  sun,  largely  filled  up, 
especially  on  the  less  refrangible  side.  At  noon  a  subordinate  maximum  has  been  found  within  the  low  sun  limits 
of  this  band  at  2.94/u,  and  a  second  one  at  2.80/<  frequently  accompanies  it,  producing  subordinate  minima  at  2.89« 
and  3.02/<.  As  the  absorption  increases  with  a  sinking  sun,  these  subordinate  maxima  disappear  to  a  very  great 
extent,  that  at  2.80.«  being  the  first  to  vanish,  as  well  as  the  quickest  to  grow,  so  that  at  noon,  on  a  cold  day,  it  not 
only  surpasses  the  maximum  at  2.94«,  but  even  begins  to  approach  that  at  3.20/*,  while,  when  the  sun's  altitude  is 
less  than  W~,  the  nearly  uniform  part  of  the  band  extends  from  2.45/<  to  3.15/i  without  a  break.  (Langiey,  Memoirs 
of  the  National  Academy  of  Science,  vol.  4,  2d  Mem.,  p.  167, 1887. ) 

The  varying  form  of  the  spectral  euergy-curve  is  doubtless  due  to  the  complex  linear  composi 
tiou  of  the  bands,  individual  lines,  or  groups  of  lines,  having  very  different  rates  of  growth  as  the 
absorbent  depth  varies;  and  to  a  corresponding  variation  in  the  emission  of  the  several  lines 
composing  a  group,  coupled  perhaps  with  the  effect  of  self-absorption  of  its  own  radiations  by  the 
outer  layers  of  a  gas  or  vapor,  is  to  be  attributed  the  change  in  the  measured  positions  of  infra-red 
bands,  noted  by  Langiey  and  abundantly  confirmed  by  Pascheu.  Of  the  two  principal  centers  of 
the  great  absorption-baud  of  water  vapor,  the  longer  at  0.5 1/t  appears  to  expand  to  still  greater 
wave-lengths  and  the  shorter  at  5.86  i  to  still  shorter  wave-lengths,  or  in  either  case  away  from 
the  common  center,  as  the  mass  of  the  absorbent  increases;  and  Paschen  shows  that  the  same 
movement  occurs  in  the  maximum  points  of  the  emission-bauds  of  water- vapor  as  the  temperature 
rises.  The  following-  table  is  quoted  from  his  paper  (  Wied.  Ann.,  Bd.  52,  S.  215, 1894),  with  wave 
lengths  approximately  corrected  by  his  latest  measures  of  fluorite  dispersion  (  Wied.  J.nra.,Bd.  53, 
S.  822). 


102 


TABLE  67. — Emission-spectrum  of  irater-vapor. 


Temperature. 

Position  of  the  highest  point  in  — 

Maximum  I. 

Maximum  II. 

Deviation. 

Wave-length. 

Deviation. 

Wave-length. 

Oxyhydrogen  flame 
Bunseu  flame,  1,470° 
1,000° 

o          / 

26    58 
27      0 

ft 

6.60 
6.57 

o        / 
28    29 
28    25.5 
28    23 

5.28 
5.34 

5.38 

600°,  approximately, 

100° 

27      2.7 
27      5.  5 

6.54         28     11 
6.50         27    51.3 

5.58 
5.87 

17°  (vapor) 
17°  (liquid) 

27      6.5 

6.48         27    48 
27    40 

5.92 
6.02 

The  relative  strength  of  the  maxima  of  the  strongest  emission-bauds  in  the  spectral  energy- 
curve  of  water-vapor  at  different  temperatures  follows  closely  the  relation  between  the  corre- 
sponding intensities  at  the  same  wave-lengths  and  temperatures  in  the  spectrum  of  a  black  body; 
and  the  absolute  intensities  are  not  far  behind.  This  indicates  that  at  these  points  the  radiant 
power  of  a  comparatively  small  mass  of  vapor  is  nearly  perfect;  but  this  can  not  be  said  of  the 
borders  of  the  bands,  and  we  need  not  expect  that  any  completely  consistent  rule  sho.uld  be  fol- 
lowed in  their  variation.  The  bolometer  covers  several  alternations  of  radiant  or  absorbent 
spectral  lines  and  their  intervals,  giving  us  the  sum  of  the  series.  If  the  lines  broaden  and  the 
intervals  fill  up  until  the  lines  coalesce  completely,  the  limits  of  perfect  radiation  or  absorption 
widen,  and  if  the  band  is  one-sided,  its  center  changes  its  position  in  the  spectrum.  So  long  as 
there  is  no  disintegration  of  atomic  groupings  increased  heat  may  bring  out  new  lines  and  give 
greater  complexity  to  the  spectrum,  changing  the  aspect  of  a  group.  Since  the  centers  of  several 
aqueous  bands  shift  to  longer  waves  as  the  temperature  rises,  their  structure  probably  resembles 
that  of  the  A  and  B  groups  of  oxygen,  in  beginning  with  strong  lines  on  the  side  of  the  short 
waves  and  gradually  fading  out  in  a  long  series  of  feebler  and  more  widely  separated  lines  on  the 
side  of  the  long  waves.  The  shifting  of  the  center  of  Maximum  II  (Table  G7)  is  in  the  opposite 
direction,  and  is  also  more  rapid  than  that  of  I.  In  II  the  relatively  greater  increase  of  radiations 
of  short  wave  length  with  rising  temperature  may  assist,  as  suggested  by  Paschen,  but  only  by 
aiding  a  process  depending  on  structural  detail  of  the  band,  which  here  fades  out  in  the  same 
direction  as  the  shifting  of  the  maximum  ordinate  in  the  spectral  energy-curve  of  a  black  body. 
In  I  a  similar  greater  increase  of  short  than  of  long  waves  can  not  entirely  overcome  the  struc- 
tural shifting  to  the  side  of  the  long  waves;  and  the  same  is  true  of  the  band  A",  while  fl  and  V, 
situated  in  a  part  of  the  spectrum  where  the  rate  of  increase  of  intensity  with  temperature  varies 
rapidly  with  the  wave-length  at  flame  temperatures,  have  the  structural  shifting  toward  long 
waves  slightly  overbalanced  by  the  more  general  formal  change,  as  is  shown  in  the  next  table,  also 
taken  from  Paschen's  work  ( Wied.  Ann.,  Bd.  52,  S.  226),  the  wave-lengths  corrected  as  before. 

TABLE  68. — Emission-spectrum  of  water-vapor. 


Temperature  : 

c 

/ 

u 

Oxyhydrogen  flame 

Deviation  30 

26.0 

A  =  2.75 

Bunsen  flame 

30 

25. 

5 

2.77 

Over  1,000°                 -X 

30 

26. 

0 

2.75 

500° 

30 

29 

2.65 

100° 

30 

30. 

8 

2.59 

Oxyhydrogen  flame 

f                    30 

52. 

0 

1.78 

Bnnsen  flame             fl< 

30 

51. 

5 

1.81 

Over  1,000° 

30 

51. 

0 

1.84 

Oxyhydrogen  flame 

[                   31 

3 

1.34 

Bnnsen  flume              W< 

31 

2 

1.38 

Over  1,000° 

31 

2 

1.38 

103 

For  the  wave-lengths  of  the  last  three  bands  we  need  not  depend  on  transformations  from 
dispersion  measures,  since  these  maxima  can  be  identified  in  the  grating- spectrum  of  the  Bunseii 
flame.  Paschen's  curve  ( Wied.  Ann.,  Bd.  50,  Taf.  IX,  fig.  8)  gives  the  following  values: 

i  Group  W  extends  from  l.33jn  to  1.50//. 
'    I  Subordinate  maxima,  1.35//  and  1.42#;  mean,  1.385//. 

(  Group  O,  extends  from  1.75yu  to  2.10//. 
'   }  Subordinate  maxima,  l.SO//,  1.86//,  and  1.97^;  mean,  1.877//. 

(  Group  A"/ extends  from  2.42yu  to  3.02//. 
'   1  Subordinate  maxima,  2.51//,  2.70//,  and  2.83 /u;  mean,  2.680//. 

In  the  absorption-bands  of  the  solar  spectrum,  the  deepest  depression  of  D,  extends  from 
1.81/<  to  1.87 /u  according  to  Langley  ("Researches  on  solar  heat,"  Prof.  Papers  of  the  Sig.  Sen\,  No. 
15,  p.  228,  Washington,  1884),  and  the  extension  of  the  group  on  the  side  of  the  long  waves  is 
much  feebler  than  in  the  emission-baud  of  the  Buuseii  flame.  The  subordinate  maximum  of  A  at 
2.83/i  in  the  flame  spectrum  appears  to  agree  with  the  minor  band  in  the  solar  spectrum,  called  xi 
by  Laugley,  the  wave-length  of  which  was  originally  given  as  2.89^  (ante,  p.  101).  That  at  2.70// 
agrees  in  position  with  one  of  the  bauds  of  CO2. 

Captain  Abney  and  Lieutenant-Colonel  Festing  have  photographed  a  continuous  spectrum 
through  several  inches  of  water,  getting  the  absorption-spectrum  to  a  wave-length  of  l/<  ("Atmos- 
pheric absorption  in  the  infra-red  of  the  solar  spectrum,"  Proc.  R.  Soc.  London,  vol.  35,  p.  80, 1883). 
Three  inches  of  liquid  water  give  the  following  bauds:  (1)  begins  with  a  strong,  sharp  edge  at 
0.735/<  and  extends  to  0.765yU,  fading  out  thence  on  the  side  of  the  long  waves,  very  gradually. 
Great  A  is  included  in  its  diffuse  margin.  (2)  in  like  manner  begins  with  a  strong,  sharp  edge  at 
0.833;/,  between  Brewster's  A"  and  Y,  and  fades  out  gradully  toward  the  long  waves,  the  principal 
part  of  the  baud  extending  from  0.833/t  to  0.875//.  The  strong  pair  of  lines,  A,  in  the  solar 
spectrum,  due  to  calcium,  wave-lengths  0.854/t  and  0.866/Y,  is  included  in  the  diffuse  margin.  (3)  is 
a  very  strong  band  between  wave-lengths  0.942//  and  0.986//,  occupying  nearly  the  same  position 
as  the  bands  in  the  solar  spectrum,  called  p  a  t  by  Abney.  It  is  bordered  by  hazy  extensions 
and  broadens  to  0.88yu,  when  the  depth  of  water  is  increased  to  1  foot.  These  three  bands  are  not 
composed  of  fine  lines,  but  are  diffuse,  and  they  appear  in  photographs  of  the  solar  spectrum, 
superposed  on  groups  of  lines,  and  becoming  very  strong  when  the  relative  humidity  approaches 
saturation.  The  authors  say : 

Besides  these  linear  absorptions,  photographs  taken  on  days  of  different  atmospheric  conditions  show  banded 
absorptions  superposed  over  them.  :  '  On  a  fairly  dry  day  the  banded  absorption  is  small,  taking  place  princi- 

pally between  A9420  and  A9800;  a  trace  of  absorption  is  also  visible  between  A 8330  and  A9420.  On  a  cold  day,  with  a 
northeasterly  wind  blowing  [this  being  for  England  the  dry  quarter],  and  also  at  a  high  altitude  on  a  dry  day, 
these  absorptions  nearly,  if  not  quite,  disappear.  When  the  air  is  nearly  saturated  with  moisture,  *  *  * 

except  with  very  prolonged  exposure,  no  trace  of  a  spectrum  below  A8330  can  be  photographed.    (Loc.  cit.,  pp.  80-81.) 

Comparing  these  observations  with  those  of  Liveing  and  Dewar  on  the  two  kinds  of  oxygen 
bands,  linear  and  diffuse,  and  with  the  facts  adduced  here  which  show  that  there  is  a  very  large 
increase  in  the  absorptive  power  of  aqueous  vapor  when  nearly  saturated,  it  seems  probable  that 
the  diffuse  bands  of  liquid  water  and  of  a  saturated  vapor  are  due  to  the  complex  aqueous 
molecules  discovered  by  Ramsay  and  Shields,  while  the  groups  of  fine  lines  in  nearly  the  same 
positions  in  the  spectrum  belong  to  simpler  molecules  which  no  longer  exist  in  the  liquid  state, 
but  are  present  in  variable  proportion  in  the  vapor,  according  to  the  temperature  and  the  degree 
of  saturation. 

Abney  and  Festing  in  another  paper  ("The  influence  of  water  in  the  atmosphere  on  the  solar 
spectrum,"  etc.,  Proc.  R.  Soc.  London,  vol.  35,  p.  328, 1883)  give  spectral  energy-curves  for  the  crater 
of  the  positive  carbon  of  an  arc-light  after  absorption  by  various  thicknesses  of  liquid  water, 
obtaining  evidence  that  nearly  all  of  the  great  cold  bands  in  the  solar  spectrum  to  3/<  are  due  to 
water.  The  liquid  absorption  bands  are,  however,  much  more  intense  than  the  vaporous  ones, 
and  coalesce  to  form  extensive  regions  of  complete  absorption.  In  addition  to  these  curves,  rough 
photographs  of  the  solar  spectrum  to  a  wave-length  of  2.2/n  were  taken  on  cold  dry  days,  which 
confirm  the  presence  of  all  of  these  water-bands  and  give  their  positions  more  accurately  than 
the  heat  measures  made  in  the  spectrum  with  a  linear  thermopile  whose  aperture  was  one-fiftieth 
of  the  length  from  the  D  line  to  the  end  of  the  infra-red  spectrum  from  a  glass  prism.  In  the 


104 


following  table  these  thermal  measures  (loc.  cit.,  p.  332)  are  exhibited  as  percentage-transmissions 
iii  the  last  three  columns : 

TABLE  69. — Transmission  of  spectrum  by  liquid  i.cater. 


Radiation 
through 
empty  glass 
celL 

Deflection  through  — 

Transmission  l>y— 

J  inch 
water. 

1J  inches 
water. 

24  inches 
water. 

£  inch 
water. 

1J  inches 
water. 

24  inches 
water. 

Per  cent. 

Per  cent. 

Per  cent. 

At  .D-line  in  yellow 

7.5 

7.3 

6.8 

3.2 

97 

91 

43 

Maximum  in  orange-yellow 

8.7 

8.7 

8.5 

4.0 

100 

98 

46 

Orange  band 

10.0 

9.2 

8.8 

3.7 

92 

88 

37 

Maximum  in  red 

16.7 

16.7 

16.0 

10.7 

100 

96 

64 

Red  baud  (near  A) 

19.3 

18.5 

17.0 

2.3 

96 

88 

12 

Maximum  near  1" 

22.8 

22.8 

20.6 

1.4 

100 

90. 

6 

Baud  between  A"  and  Y 

24.6 

23.0 

21.0 

0.3 

93 

85 

1 

Maximum  (Herschel's  a) 

25.4 

24.7 

22.0 

0.0 

97 

87 

Band  (Abney's  p  6  r) 

27.7 

21.5 

5.3 

78 

19 

Maximum  (HerscheFs  /?) 

30.0 

26.3 

10.0 

88 

33 

Band  (Abney's  #) 

[26.  7] 

18.  5 

0.5 

69 

2 

Maximum  (Herschel's  y) 

[24.9] 

19.0 

7.0 

76 

28 

Band  (Abuey's  W) 

18.5 

*    0.7 

0.0 

4 

0 

Maximum  (Herscnel'sS) 

11.6  - 

3.0 

26 

Band  (Langley's  fi) 

[5.4] 

0.0 

0 

Maximum  (Herschel's  £) 

[2.9J 

1.5 

52 

Band  (Langley's  X) 

0.0 

0 

The  extreme  infra-red  region  of  the  spectrum,  beyond  the  great  water-band,  has  recently 
been  explored  by  Prof.  H.  Eubens  and  E.  Aschkinass  ( Wied.Ann.,  Bd.  64,  S.  584, 1898  ;  translated 
in  the  Astrophys.  Journ.,  vol.  8,  p.  176).  The  radiation  from  the  mantle  of  a  zirconium  burner 
passing  through  a  cast-iron  tube  75  cm.  long,  "heated  above  100°  by  four  Buusen  burners  beneath 
it,"  and  fed  with  a  permanent  stream  of  aqueous  vapor,  was  formed  into  a  spectrum  by  a  prism  of 
sylvite,  which  at  a  wave-length  of  18//  still  transmitted  "  some  70  per  cent.,  and  at  20//  some  30 
per  cent.,  of  the  incident  radiation."  The  general  results  are  thus  stated  by  the  authors  (Astropliys-. 
Journ.,  vol.  8,  p.  190)  : 

Water-vapor  shows  only  faint  absorption  in  the  spectral  region  between  A  =  9/i  and  A  =  ll/u,  as  compared  with 
shorter  and  longer  waved  parts  of  the  infra-red.  From  this  follows  the  minimum  [emission]  observed  in  the  emis- 
sion [curve  of  hot  water-vapor]  at  A  =  10.7//.  Beyond  11/i  the  absorption  begins  to  increase  and  becomes  almost 
total  at  A=20,u,  whereby  the  maximum  observed  in  the  emission  [from  hot  water-vapor]  at  A  =  13.1/i  is  explained. 
[The  transferring  of  the  maximum  from  20/i  in  absorption  to  13/i  in  emission  is  about  what  might  be  expected  from 
the  rate  of  increase  of  the  radiation  of  a  black  body  with  shortening  wave-lengths,  combined  with  the  larger  trans- 
mission of  the  shorter  waves  by  sylvite  in  this  part  of  the  spectrum.]  In  the  region  between  11/z  and  IS/n,  water- 
vapor  possesses  six  conspicuous  maxima  of  absorption,  which  have  according  to  our  observations  the  wave-lengths 
A  =  11.6/4,  12.4/1,  ISAju,  U.Sju,  lo.lju,  and  17.5,u. 

The  intensities  of  absorption  of  these  six  bands  are  10,  20,  28,  43,  63,  and  88  per  cent.,  respec- 
tively; while  at  20,w,  as  stated,  the  absorption  is  nearly  100  per  cent.  Beyond  this  point,  at  wave- 
lengths 24.4 w,  aqueous  vapor  exerts  only  a  very  slight  absorption  (Eubens  and  Nichols,  Pliys.  Rev., 
vol.  4,  p.  322,  1897;  also  Wied.  Ann.,  Bd.  60,  S.  418,  1897).  Since  air  was  not  excluded  from  the 
apparatus,  it  is  possible  that  the  total  absorption  at  20 jn  may  have  some  other  origin  (see  p.  113). 

It  will  be  evident  that  the  interrelations  of  aqueous  absorption  and  radiation  in  terrestrial 
meteorology  must  be  complex.  The  radiations  of  clouds,  the  sea,  and  to  a  considerable  extent 
those  of  moist  earth  and  vegetation  do  not  difl'er  much  from  the  radiant  emission  of  a  solid  black 
body  whose  spectral  energy-curve  has  its  maximum,  at  terrestrial  temperatures,  in  the  immediate 
vicinity  of  the  chief  aqueous  absoiption-bands.  The  depletion  of  radiation  is  especially  great  if 
the  coincidence  of  maximum  radiation  and  principal  absorption  is  exact ;  but  the  position  of  the 
maximum  of  aqueous  absorption  in  the  spectrum  varies  with  the  amount  of  water  and  with  its 
physical  state.  The  position  of  the  maximum  of  the  unabsorbed  energy-curve  also  varies  with 
the  temperature  of  the  radiating  body  and  of  the  surface  to  which  it  radiates.  Thus  there  is  room 
for  a  great  variety  of  combinations. 

The  apparent  absorption  of  a  layer  of  heated  vapor  is  a  differential  one,  being  the  resultant 


105 

of  a  series  of  operations  made  up  of  the  sum  of  the  original  radiation  of  the  body  behind  the 
vapor,  minus  the  absorption  exerted  upon  this  radiation  by  the  vapor,  plus  the  emission  of  the 
vapor's  own  radiation,  diminished  by  the  absorption  of  the  radiation  from  deeper  vaporous  layers 
by  the  vapor  subsequently  traversed.  Since  the  vaporous  emission  varies  with  the  temperature, 
the  apparent  absorption  of  the  hot  vapor  likewise  varies,  except  at  temperatures  too  low  for 
appreciable  emission.  This  is  very  well  shown  in  the  series  of  absorption  and  emission  curves 
for  carbon  dioxide  at  temperatures  from  180°  to  480°,  given  by  Paschen  (Wied.  Ann.,  Bd.  51, 
Taf.  1,  fig.  8,  1894).  At  the  highest  temperature  the  apparent  absorption  is  almost  nothing,  the 
radiant  emission  by  the  hot  gas  having  counteracted  its  absorption.  I  have  already  noted 
(ante,  p.  53)  that  this  observation  may  be  used  in  constructing  a  curve  of  temperature  and 
depth  at  which  absorption  exactly  compensates  radiation.  Another  point  on  such  a  curve  is 
given  by  the  present  measures  (ante,  p.  54),  which  show  that  for  a  temperature  of  126°  C.  the 
effective  radiating  depth  of  carbon  dioxide  is  only  a  little  over  3  feet,  let  us  say  100  cm. 
Pascheu's  measurement  gives  the  temperature  of  480°  C.,  corresponding  to  a  depth  of  7  cm. 

ABSORPTION   OF   RADIATION   BY   CARBON  DIOXIDE. 

Prof.  Kuut  Angstrom  ( Wied.  Ann.,  Bd.  39,  S.  300, 1890;  see  also  the  preceding  article,  begin- 
ning p.  267),  quoting  observations  by  Lecher  which  show  that  the  solar  rays,  after  sifting  by  an 
air-mass  of  three  atmospheres,  are  almost  entirely  deprived  of  those  ether- waves  which  are  sus- 
ceptible of  absorption  by  a  moderate  depth  (1.05  meters)  of  carbon  dioxide,  concludes  that,  since 
the  mean  quantity  of  this  gas  in  the  atmosphere  is  less  than  0.02  j>er  cent.,  corresponding  to  a 
vertical  depth  of  less  than  1.5  meters  of  CO2,  and  in  three  atmospheres  to  less  than  4.5  meters,  the 
transmission  by  one  meter  of  carbon  dioxide,  within  the  limits  of  the  CO2  absorption-bands,  is 
between  20  and  30  per  cent.,  because  the  transmission  of  these  particular  rays,  after  a  preliminary 
sifting  through  0.5  meters  of  CO2,  has  been  found  to  follow  the  simple  exponential  law : 

i  =  Ix  /'", 

where  I  is  the  initial  intensity  of  the  limited  radiation,  t  the  transmission  by  unit-mass,  m  the 
actual  mass  of  carbon  dioxide  (measured  as  the  depth  in  meters  of  CO2  traversed  by  the  rays),  and 
i  the  resultant  intensity  after  absorption,  by  which  law  this  degree  of  trail  smissibility  secures  the 
extinction  of  these  rays.  The  strength  of  the  chief  carbon  dioxide  band  in  the  solar  spectrum 
also  appears  to  agree  with  what  might  be  anticipated  from  the  known  absorbent  mass  of  this  gas 
in  the  Earth's  atmosphere,  and  the  assumption  that  carbon  dioxide  gas  has  a  simple  molecule 
under  every  degree  of  dilution  and  that  its  absorption  depends  entirely  upon  the  mass  of  gas 
traversed,  is  warranted. 

One  other  assumption,  however,  is  less  commendable.  While  such  small  transmissions  as  20 
to  30  per  cent,  are  the  rule  in  limited  regions,  or  bauds,  in  the  infra  red,  it  is  not  permissible  to 
apply  them,  as  Angstrom  has  done,  to  the  entire  infra-red  of  the  solar  spectrum,  thereby  raising 
the  estimated  solar  constant  to  four  small  calories.*  It  must  be  understood  that  the  absorption  of 
20  to  30  per  cent,  is  the  mean  absorption  of  a  series  of  bands  which  include  special  rays  totally 
absorbed,  as  well  as  intermediate  ones  which  go  free. 

Angstrom's  result  indicates  that  about  4.5  meters  of  carbon  dioxide  is  sufficient  to  almost 
completely  cut  off  the  radiations  absorbable  by  this  gas,  and  taken  in  conjunction  with  Keeler's 
observation  (Am.  J.  Sci.  (3),  vol.  28,  p.  196,  Sept.,  1884)  that  3.4  meters  of  carbon  dioxide  absorb 
35.8  per  cent,  of  the  radiation  from  a  Bunsen  burner  name,  the  two  ought  to  give  approximately 
the  relative  values  of  CO2  and  H2O  radiations  from  this  flame  whose  spectrum  is  purely  one  of 
bands.  We  should  anticipate  from  these  facts  that  not  over  40  per  cent,  of  Bunsen  flame  radia- 
tion is  due  to  carbon  dioxide,  the  rest  coming  mainly  from  water- vapor.  This  differs  somewhat 
from  the  relative  areas  of  the  sums  of  the  respective  maxima  in  Pascheu's  curve  of  energy  in  the 
spectrum  of  the  Bunseu  flame,  but  as  the  composition  of  ordinary  illuminating  gas  is  variable, 


"The  application  of  the  method  by  which  Angstrom  obtains  this  value  leads  to  the  absurd  result  that  over 
60  per  cent,  of  the  original  solar  radiation  is  contained  in  the  spectral  region  occupied  by  the  bands  of  carbon 
dioxide.  The  limits  of  these  bauds  have  now  been  ascertained,  and  it  is  certain  that  they  do  not  cover  a  length  of 
the  solar  spectrum  possessing  more  than  a  small  fraction  of  this  proportion  of  total  radiant  energy. 


106 


some  range  in  the  aqueous  component  of  flame-radiation  must  be  expected  from  this  cause;  and, 
besides  this,  the  temperature  of  the  flame  is  not  a  constant  quantity,  while  the  relative  radiations 
of  the  different  components  do  not  vary  with  the  temperature  according  to  the  same  law.  Never- 
theless, I  believe  that  the  chief  cause  of  the  discrepancy  is  the  considerable  absorption  by  the 
fluorite  of  Paschen's  prism  of  those  emission-bands  of  aqueous  vapor  which  are  of  greater  wave- 
length than  those  carbon  dioxide  bands  which  furnish  the  larger  part  of  the  emission  at  high  tem- 
peratures. Separating  the  CO.  and  H2O  bands  in  Paschen's  curve  (  Wiefl.  Ann.,  Taf.  IX,  fig.  6), 
I  found  the  relative  areas  were : 

CO2:H2O  =  115:1<)7 

Making  allowance  for  fluorite  absorption  increases  the  proportion  of  aqueous  radiation,  and 
reverses  the  ratio.  Hence  less  than  half  the  radiation  of  the  hot  gases  of  the  Bunsen  flame  is  due 
to  carbon  dioxide. 

The  growth  of  the  band-emission,  as  temperature  rises,  agrees  so  nearly  with  the  rate  of 
increase  of  the  total  radiation  of  carbon  dioxide  that  another  reason  is  added  to  Paschen's  argu- 
ment in  favor  of  the  absolute  discontinuity  of  its  spectrum.  Zollner  and  Wu'llner  having  reached 
the  conclusion  that  a  gaseous  layer  of  infinitely  great  depth  would  send  out  a  continuous  spec- 
trum from  the  broadening  of  the  lines,  a  conclusion  which  presupposes  that  emission  and  absorp- 
tion are  never  zero  for  any  wave-length,  Paschen  tested  the  hypothesis  by  observing  the  absorption 
of  33  cm.  of  carbon  dioxide  at  the  maximum  in  the  spectrum  of  an  incandescent  lamp  (1  =  1.4/.;), 
a  point  quite  outside  the  special  regions  of  absorption  for  this  gas.  Xo  difference  greater  than 
one  part  in  four  thousand  could  be  found  between  the  absorption  of  air  and  CO2  at  this  point. 
"It  is  improbable  that  such  absorptions,  if  they  were  present,  should  be  the  same;  it  is  more 
likely  that  both  are  zero.  However,  in  consequence  of  the  moisture  of  the  air,  a  small  and 
equal  absorption  may  have  been  present  every  time."  (  \Vied.  Ann.,  Bd.  51,  S.  33.) 

"The  fact  that  CO2  exerts  an  absorption  which  at  any  other  spectral  positions  than  those  of 
its  absorption-bands  is  zero  within  the  limits  of  errors  of  observation  stands  in  connection  with 
another  fact  that  the  breadth  of  the  absorption-bauds  in  question  does  not  grow  with  increasing 
depth  of  the  layer."  The  breadth  of  the  principal  CO,  absorption-band,  at  A  =  4.25//,  remained 
unchanged  when  the  thickness  of  the  cold  gas-layer  was  increased  from  0.3  cm.  to  33.0  cm.,  the 
absorption  of  the  maximum  meanwhile  increasing  from  55  to  90  per  cent.  "For  line  spectra  it 
follows  *  *  *  that  with  increasing  thickness  of  the  gas-layer  in  emission  the  lines  only  become 
brighter,  but,  in  general,  can  not  spread  themselves  over  the  entire  spectrum."  (Loc.  tit.,  p.  34). 
This  does  not  prevent  the  greatest  variety  as  to  strength  and  rates  of  growth  in  such  spectral  lines 
as  those  of  water- vapor,  but  the  carbon  dioxide  spectrum  is  much  simpler.  Besides  the  two  bands 
discovered  by  Knut  Angstrom 

(1)  at  2.3/<  to  3.0/*,  maximum  2.7/<,  and 

(2)  at  3.9/i  to  4.7/v,  maximum  4.25//, 

Rubens  and  Aschkinass  have  discovered  a  third  strong  band  in  the  extreme  infra-red.  With  a 
thickness  of  a  little  more  than  20  cm.  of  CO2,  "the  whole  region  of  absorption  is  limited  to  the 
interval  from  12.5yu  to  16;<,  with  the  maximum  at  14.7/f.  Aside  from  this  region  not  the  slightest 
absorption  could  be  detected  between  8yu  and  20//,  even  when  the  box  was  completely  filled 
with  carbon  dioxide,"  giving  a  depth  of  65  cm.  (Astrophys.  Journ.,  vol.  8,  p.  191,  1898.) 
The  absorption  at  different  points  in  baud  (3)  (loc.  tit.,  p.  189,  fig.  9)  is  as  follows: 

[Source,  zirconium  burner — Absorption  by  20  cm.  -(-  of  COj.] 


Wave 
length. 

Absorp- 
tion. 

Wave- 
length. 

Absorp- 
tion. 

Wave- 
length. 

Absorp- 
tion. 

/' 

Per  cent. 

/' 

Per  cent. 

/' 

Per  cent. 

12.5 

1 

14.0 

28 

15.0 

70 

13.0 

4 

14.5 

67 

15.5 

30 

13.5 

10 

14.7 

75 

16.0 

2 

The  absorption  at  the  center  of  band  (2),  according  to  Paschen  (Wied.  Ann.,  Bd.  51,  S.  9), 
amounted  to  30  per  cent,  from  the  small  trace  of  carbon  dioxide  in  the  air  of  the  room.     This  was 


107 

increased  to  89  per  cent,  by  the  addition  of  a  7  cm.  layer  of  the  gas,  but  after  this  absorption  was 
reached,  further  increase  of  the  layer  up  to  33  cm.  made  little  difference.  At  baud  (1)  (loc.  cit., 
p.  10),  an  initial  absorption  of  10  to  20  per  cent,  by  the  air  of  the  room  was  increased  to  about  30 
per  cent,  by  the  7  cm.  layer,  and  to  43  per  cent,  by  a  layer  of  CO2  33  cm.  thick. 

Owing  to  the  very  local  distribution  of  the  bands  of  carbon  dioxide,  the  total  amount  of  its 
absorption  varies  greatly  with  the  temperature  of  the  radiant  source  on  whose  emanations  the 
absortion  of  the  gas  is  exercised.  Assuming  that  the  absorption  by  a  thickness  of  1  inch  of  CO2 
at  30  inches  pressure  is  identical  with  that  of  48  inches  of  CO2  at  0.625  inches  pressure,  we  have 
from  Tyndall's  measures  (Contributions  to  Molec.  Phys.7  pp.  37  and  170): 

Temperature  of  source  of  radiation  100°  C. ;  1  inch  of  CO2*  absorbs  2.2  per  cent. 

a  a  tt  a  2       it  a  a         3^4.        .. 

"  "  "  270°  C.;  1      "  "  "         6.3       " 


(t  tt  it  tt  •>  «  It  it 


.6        « 


Hence  the  absorption  of  radiation  from  the  source  at  higher  temperature  is  two  to  three  times 
as  great  as  for  the  radiation  from  the  low-temperature  source.  The  reason  for  this  is  seen  on  com- 
paring the  spectral  energy-curves  of  the  sources.  The  chief  baud  of  carbon  dioxide  (A.  =  4.25/<) 
falls  near  the  maximum  ordinate  in  the  curve  for  270°,  but  affects  a  relatively  insignificant  region 
of  the  spectrum  of  a  body  at  100°  C.  On  the  other  hand,  the  chief  absorption  by  water-vapor 
agrees  more  nearly  in  wave-length  with  the  maximum  of  the  source  of  lower  temperature, 
whose  radiation,  in  consequence,  is  relatively  more  depleted  in  passing  through  moist  air  than 
that  of  a  hotter  body. 

From  the  figures  just  given  we  may  infer  that  the  amount  of  carbon  dioxide  in  100  meters  of 
air  at  normal  pressure  absorbs  about  2.5  per  cent,  of  the  radiation  from  a  source  at  100°  C. 

APPLICATION  OF  THE  FOREGOING  STUDY  OF  GASEOUS  ABSORPTION  TO  THE  RESULTS 

OF  LABORATORY  EXPERIMENTS. 

We  are  now  ready  to  correct  the  measured  values  of  apparent  gaseous  radiation,  obtained  in 
Method  C,  by  allowance  for  the  modifications  introduced  by  gaseous  absorption. 
By  Table  48,  p.  71,  the  apparent  radiation  of  141.8  cm.  of  carbon  dioxide  was: 

At  excess  50°  C.  r  =  93  x  (10)-9  radim 

"        "      80°  C.  260        "  " 

"        "     100°  c.  482  « 

• 

According  to  the  data  in  the  chapter  on  screens,  the  corresponding  measured  radiations  of  a  screen 
of  sooted  copper  (the  initial  temperature  being  35°  C.)  were: 

At  excess  50°  C.  (358°  absol.  T.)         r  =  1335  x  (10) ~9  radim 
"        "       80°  C.  (388°  absol.  T.)  2321        "  " 

"     100°  C.  (408°  absol.  T.)  3095        "  « 

From  the  curve  (fig.  18),  representing  the  absorption  by  carbon  dioxide  of  radiation  from  sooted 
copper  at  100°  C.,  founded  on  the  observations  of  Tyndall,  already  cited,  it  may  be  inferred  that 
a  5-foot  layer  of  CO.  intercepts  18.4  per  cent,  of  the  rays.  The  corresponding  absorptions  for  the 
sources  at  lower  temperatures  will  be  about  0.8  and  1.5  per  cent,  smaller,  or  17.6  and  16.9  per  cent., 
respectively.  Hence  the  disk-radiation,  in  the  extreme  positions,  was  diminished  as  follows: 


Depth.        Temperature-excess.                Disk-radiation  absorbed  by 
60  in.                 50°  C.               1335  x  10~9  x  0.169  =  225.6 

CO: 

xio-9 

and  by  rock-salt. 

169  x  IO-9 

60 

in. 

80° 

C. 

2321  x 

10-9x 

0.176 

=  408.5 

X 

io-9 

306  x 

io-9 

60 

in. 

100° 

C. 

3095  x 

10~9  X 

0.184 

=  569.5 

X 

io-9 

427  x 

10  -9 

Compare  ante,  footnote  on  p.  87. 


108 

At  the  smallest  distance  (4^  inches)  the  disk-radiation  must  have  been  diminished  thus: 


Depth.  Temperature-excess. 
4J  in.  50°  C. 

4J  in.  80°  C. 

4    in.  100°  C. 


Disk-radiation  absorbed  by  CO-2 
1335  x  10~9  x  0.055  =    73.4  x  10~9 
2321  x!0~sx  0.055  =  127.7  x  I0~s 
3095  x  10-9  x  0.055  =  170.2  x  10-9 


and  by  rock-salt. 
55  x  10~9 
96  x  10~9 
128  x  19~9 


All  of  these  radiations  have  suffered  an  absorption  of  about  25  per  cent,  by  the  rock-salt 
plate,  *  as  given  in  the  last  columns  for  comparison  with  the  measured  radiations  also  absorbed  to 


20 
18 
16 
14 

10 
8 
6 
4 

2 


J\adiaticm  In/ 


tQ 


20 


30 


40 


50 


60 


18 


approximately  the  same  extent.     The  observed  apparent  radiations  of  the  gas  must  be  increased 
by  the  differences  of  these  numbers  and  further  increased  by  the  absorption  of  rock-salt. 

Temperature-excess.       Radiation  of  CO2  through  rock-salt,  affected  by  COj  absorption  but  corrected  for  salt. 

50°  C.  \  93  +  (169  —   55)}  x  (10)-9  -  0.75  =  207  x  10-9  4-  .75  =    276  x  10"9 

80°  c.  {260  +  (306  -    96)  |  x  (10)~9  —  0.75  =  470  x  10-9  ->  .75  =    627  x  10-9 

1000  C.  |482  +  (427  -  128)  }  x  (10)~9  -  0.75  =  781  x  10~9  4-  .75  =  1041  x  10~9 

Finally  these  values  must  be  further  corrected  for  absorption  by  4^  inches  of  carbon  dioxide. 

Only  approximate  estimates  are  available  for  this  quantity.     From  TyudalFs  Contributions, 

page  185,  Table  XXX  V,  two  minimum  values  of  the  absorption  may  be  obtained     A  layer  of  CO2 

34  inches  deep  absorbed  :^r  =  0.662,  and  one  13.1  inches  deep  absorbed  -.-g-'g  =  0.607  of  the  radia- 
tion from  a  more  distant  layer  of  the  same  gas.     A  smooth  curve  through  these  points  and  the 


*  See  my  determination  of  this  quantity.     Astronln/fi.  Journ.,  vol.  8,  p.  211,  Nov.,  1898. 


109 


zero  point,  as  in  fig.  19,  gives  an  absorption  of  -10  per  cent,  for  a  depth  of  4^  inches.  Since  a 
portion  of  the  radiation  caine  from  the  walls  of  a  metal  tube  and  was  more  transmissible  than  the 
gaseous  radiation,  and  since  the  gaseous  radiation  does  not  increase  much  after  the  third  foot,  the 
true  absorption  of  its  own  rays  by  CO2  is  certainly  greater  than  that  given,  but  I  am  unable  to  fix 


60 
40 
30 
20 

10 


im  of 


J\  aviation 


Co 


fl 


10 


15 


20 


25 


30 


35 


a  more  definite  value  for  the  absorption  by  the  smallest  depth.  Accordingly,  the  true  radiations 
which  the  bolometer  might  have  recorded,  if  it  could  have  received  the  unobstructed  emission  of 
rays  from  a  free  layer  of  carbon  dioxide  141.8  cm.  deep,  are: 


(50°)       276  x  10-9 

(80°)       627  x  10-° 

(100°)     1041  x  10-9 


.6  =  460  x  10-°  radim. 
.6  =  1045  x  10-9  radim. 
.0  =  1735  x  10-9  radim. 


Absorption  by  dry  air  being,  according  to  Tyndall,  one-ninetieth  that  of  carbon  dioxide,  the 
corresponding  disk-corrections  for  air  are,  respectively,  1,  2,  and  3  x  10~9,  and  with  further  allow- 
ance for  absorption  by  rock-salt  the  corrected  air  radiations  are: 


(50°)     (139  +  1)  x  10-9 

(80°)     (390  +  2)  x  10-9 

(100°)     (723  +  3)  x  10-9 


0.75  =  187  x  10-9  radim. 
0.75  =  523  x  10-"  radim. 
0.75  =  968  x  10-9  radim. 


The  radiation  of  carbon  dioxide  is  thus  found  to  exceed  that  of  air  in  every  case.  The  absorption 
of  rock-salt  for  air  radiation  may  differ  from  the  absorption  found  for  ordinary  low-temperature 
sources  of  radiation,  but  not  greatly,  as  the  close  agreement  of  results  obtained  by  Method  B 
without  absorbent  plates  proves.  (Ante,  p.  71.) 


110 

Tyiitlall's  comparisons  of  radiations  from  gases  dynamically  heated  (quoted  ante,  p.  76)  were 
made  with  3-foot  layers.  As  I  have  already  explained,  the  radiation  of  carbon  dioxide  is  almost 
exactly  the  same  for  a  3-foot  layer  as  for  one  of  5  feet;  but  the  air  radiation  with  the  shorter 
depth  is  reduced  proportionally.  Hence  at  50°  excess  the  radiation  of  3  feet  of  air  should  be 

J  X  188  x  10-9  =  112  x  10-'  radim, 
5 

or  about  one-fourth  of  the  corresponding  radiation  from  carbon  dioxide.  Thus  the  discrepancy 
between  my  measures  and  those  of  Tyndall  no  longer  exists  after  the  application  of  the  final 
corrections,  or,  rather,  at  first  sight,  is  turned  to  the  opposite  side. 

Theory  gives  30.5°  C.  as  the  temperature-excess  produced  by  the  dynamic  heating  of  air  at 
normal  pressure  flowing  into  an  exhausted  receiver,  and  23°  C.  is  the  corresponding  temperature 
from  the  dynamic  heating  of  carbon  dioxide.  The  observations  of  the  radiation  of  CO2  with  a 
cooling  cylinder,  however,  do  not  extend  as  low  as  this,  and  nothing  will  be  gained  by  substituting 
results  at  the  theoretical  temperature  in  the  preceding  computation. 

We  may  now  test  a  conjecture  put  forth  by  Tyndall,  that  a  residual  deflection  remaining  after 
absorption  of  the  radiation  of  a  dynamically  heated  gas  by  a  cold  layer  of  the  same  gas  is  due  to 
radiation  from  the  walls  of  the  tube  to  which  heat  has  been  transferred  by  contact.  "To  these 
latter"  [rays],  he  says,  "the  gas  in  the  second  chamber  would  be  much  more  permeable  than  to 
the  former,  and  to  these  latter,  I  believe,  the  residual  deflection  of  6°,  or  thereabouts,  is  mainly 
due.  That  this  number  turns  up  so  often,  although  the  radiations  from  the  various  gases  differ  so 
considerably,  is  in  harmony  with  the  supposition  just  made.  In  the  case  of  carbonic  oxide,  for 
example,  the  deflection  is  reduced  from  13.7°  to  6.3°,  while  in  the  case  of  nitrous  oxide  it  is 
reduced  from  19.5°  to  6.2°;  in  the  case  of  olefiant  gas  it  is  reduced  from  59°  to  10.4°,  while  in 
other  experiments  (not  here  recorded)  the  deflection  by  olefiant  gas  was  reduced  from  44°  to  6°." 
(Contributions,  p.  186.)  With  the  quadruple  ratio  (4.11  :  1),  which  1  now  give  for  the  radiations  of 
carbon  dioxide  and  air,  and  calling  the  unknown  tube  radiation  x,  the  apparent  radiations 
measured  by  Tyndall  from  36.3  inches  of  CO2  (deflection  =  16,8°),  and  from  air  (deflection  =  8°  to 

9°)  give 

(4.11  x  8.5)  -  16.8 
-53T- 

justifying  Tyndall's  supposition,  and  incidentally  supporting  the  accuracy  of  both  his  and  my 
measures.  After  wandering  through  such  a  maze  of  corrections  as  the  foregoing  an  independent 
check  does  not  come  amiss. 

The  true  radiations  from  the  dynamically  heated  gases  in  Tyndall's  work  were 

OO2,  11.0°;  air,  2.7°; 

but  the  large  deflections,  obtained  when  blackened  tubes  were  used,  were  probably  due,  as  I  have 

suggested  (ante,  p.  76-77),  to  heat  developed  by  condensation  of  gases  in  the  pores  of  lampblack. 

The  experiment  on  the  radiation  of  steam  (ante,  p.  72)  may  now  be  reduced.     The  density 

of  steam  at  135°  C.  (excess  97°),  and  at  normal  pressure,  being  -TV.,,  the  liquid  equivalent  of  142  cm., 

at  126  mm.  pressure,  is 

1        126 
142  x  533  X  760  =  0.040  381  cm., 

which  by  fig.  13  (ante,  p.  91)  will  absorb  5.1  per  cent,  of  radiation  from  lampblack  at  100°.  The 
disk  having  an  excess  of  97°,  the  correction  for  absorption  of  disk-radiation  by  vapor  and  salt  may 
be  taken  as 

2942  x  10~9  x  0.051  x  0.75  =  113  xlO'9  radim, 

and  the  apparent  radiation  of  steam,  reduced  with  the  instrumental  constant  at  the  epoch,  is 

38  x  43.8  x  10-9 '=  1664  x  10~9  radim. 

The  absorbent  layer  contained  0.000  224  cm.  of  equivalent  liquid  water  whose  absorption  exercised 
on  the  special  aqueous  rays  is  by  no  means  negligible,  as  shown  by  Tyndall's  observations  on  the 


Ill 


aqueous  absorption  of  rays  from  the  hydrogen  flame  (cited  ante,  p.  88),  from  which  ail  absorption 
of  about  1.0  per  cent,  may  be  inferred  in  the  present  case,  and  the  measurement  of  radiation  from 
a  5-foot  layer  of  low-pressure  steam,  as  finally  corrected,  is  : 

{113  +  1664  +  (0.019  x  1664)|  x  1Q-9 

-n-r-r—  -  =  2412  x  10~9  radim. 

u.  <  o 

Reduced  to  radiant  emission  to  a  complete  hemisphere,  this  becomes  0.01247  radim,  which  is  about 
81  per  cent,  of  the  constant  for  lampblack  at  the  given  temperature. 

Before  stating  the  total  gaseous  radiation  a  more  accurate  reduction  of  the  observations  at 
different  depths  than  was  possible  before  shall  be  given. 

From  the  curve  (fig.  18)  the  values  of  CO2  absorption  of  disk-radiation,  corresponding  to  even 
feet,  are  taken  and  used  to  correct  the  percentages  in  Table  40.  By  page  108,  the  correction  to 

299 
CO.  radiation  for  absorption  of  disk-radiation  (both  being  absorbed  by  rock-salt)  is  rg^  =  62  per 

cent.  This  will  appear  in  the  final  column  of  the  next  table,  the  other  numbers  in  this  column 
being  derived  from  it. 

TABLE  70. 


Depth  of 
C02 

CO2  absorption 
of  disk-radiation.           ~a' 

6—  «—  «i 

Correction 
c  =  b  X  62 
per  cent. 

12.9 

Inches. 

Per  cent. 

Per  cent. 

Per  cent.             Per  cent. 

4i 

ai=  5.  5 

0 

0 

0 

12 

a-f=  9.  6 

4.1 

31.8 

+19.7 

24 

a:i=13.  9 

8.4 

65.1 

+40.4 

36 

a4=16.  4 

10.9 

84.5 

-|-52.  4 

48 

a5=17.  8 

12.3 

95.3 

+59.1 

60 

Ort=18.  4 

12.9 

100.0 

+62.0 

Applying  the  corrections  in  the  last  column  to  the  observed  radiations  we  have : 

TABLE  71. 


Depth. 

0.35  foot. 

1  foot. 

2  feet. 

3  feet. 

4  feet. 

5  feet. 

Per  cent. 

Per  cent. 

Per  cent. 

Per  cent. 

Per  cent. 

Per  cent. 

CO2  radiation 

0 

33.3 

72.0 

98.7 

100.0 

97.1 

Correction  (c) 

+19.7 

+40.4 

+52.4 

+59.1 

+62  0 

Sum 

53.0 

112.4 

151.1 

159.1 

159.1 

Corrected  CO2  ra- 

diation express- 

• 

ed  as  a  percent- 

0 

33.3 

70.6 

95.0 

100.0 

100.0 

age  of  the  high- 

est value. 

The  air  values  in  Table  40  will  not  be  changed  appreciably  by  a  correction  for  the  absorption 
of  disk-radiation  by  air.  Accordingly,  the  percentage  of  radiation  from  different  depths  of  the 
two  gases  may  now  be  finally  stated. 

TABLE  72. 


CO2                 Air. 

C02 

Air. 

Feet. 

Centimeters. 

0 

100               100 

125               100             125 

4 

100                80            100              100             100 

3 

99                60             75                91.5           75 

2 

80                40 

50 

70.5 

50 

1 

48                20 

25 

40.5 

25 

i 

2.5 

6 

2.5 

112 


Values  obtained  with  the  factor  E2  (p.  23),  and  representing  the  actual  radiation  falling  upon 
the  bolometer  as  measured  in  absolute  units,  are  reduced  to  hemispherical  emission  by  multiplying 
by  the  factor : 

2  n  X  (28.7)' 
0.19x5.2685  ~ 

An  approximate  conception  of  the  relations  between  the  total  radiation  passing  through  the 
unit  of  surface  in  the  unit  of  time,  the  temperature,  and  the  depth  from  which  radiation  proceeds, 
may  be  obtained  for  carbon  dioxide  and  air  by  combining  the  variations  from  change  of  temperature 
with  those  for  change  of  depth,  which  is  done  in  the  following  table  (73)  completing  the  experi- 
mental part  of  this  research. 

TABLE  73. 


Depth.      125  cm. 

100  cm. 

75  cm. 

50  cm. 

25  cm. 

2.  5  cm. 

Air. 

CO2. 

Air.     CO2. 

Air. 

CO,. 

Air. 

CO.,.     Air. 

C02. 

Air. 

CO2. 

o 

100 

.00442 

.00897 

.  00353  .  00897 

.  00265 

.  00821 

.00176  .00632  .00088 

.  003,3 

.00009 

.  00054 

90 

.  00325 

.00697 

.  00260  .  00697 

.  00195 

.  00638 

.  00130 

.  00491  .  00065 

.00282 

.00007 

.00042 

80 

.  00238 

.  00540 

.00190  .00540 

.  00143 

.  00494 

.  00095 

.00381  :  .00048 

.  00219 

.  00005 

.  00032 

70 

.00173 

.  00417 

.  00138  .  00417 

.  00104 

.  00382 

.  00069  .  00294 

.  00035 

.  00169 

.  00004 

.00025 

60 

.  00123  .  00319 

.  OOC99  .  00319 

.  00074 

.  00292  .  00049  .  00225 

.  00025 

.  00129 

.00002 

.00019 

50 

.00086 

.00238 

.  00068  .  00238 

.  00051 

.  00218  .  00034 

.  00168 

.  00017 

.  00096 

.  00002 

.00014 

40 

.00056 

.00169 

.  00045  .  00169 

.00034 

.  00155 

.  00023 

.00119 

.00011 

.  0006S 

.  00001 

.  00010 

30  .  00035 

.00111 

.00028  .00111 

.  00021 

.  00102  .  00014 

.00078 

.  00007 

.  00045 

.  00001 

.00007 

20  .00019 

.00064 

.  00016  .  00064 

.  00012 

.  00059  .  00008 

.00045 

.  00004 

.  00026 

.  00000 

.  00004 

10  .00008 

.00027 

.  00006  .  00027 

.  00005 

.00025  .00003  .00019  .00002 

.00011 

.00000 

.00002 

These  values  in  fractions  of  a  radim  are  plotted  in  Fig.  20. 

At  100°  C.  excess  of  temperature,  and  at  a  somewhat  greater  excess  above  the  freezing  point, 
air  1  cm.  deep  radiates  0.000  036  radim,  or  0.000  000  36  radim  per  degree.  With  an  excess  of 
only  1°  C.  the  radiation  may  be  estimated  as  'about  0.000  000  06  radim.  These  quantities  are 
considerably  smaller  than  the  0.000  001  14  radim  found  by  Professor  Hutchins  (Am.  J.  Sci.  (3) 
vol.43,  p.  362,  1892),  who,  however,  did  not  dry  his  air.  Moreover,  as  has  been  shown,  Professor, 
Hutchius  underestimated  the  depth  of  the  radiant  layer  of  gas,  which  makes  his  measurement 
of  radiation  per  unit  of  depth  too  large.  On  the  other  hand,  my  values  exceed  that  deduced  by 
Maurer  from  meteorological  considerations,  namely,  0.000  000  Oil  6  radim.  The  difference  here  is 
very  likely  due  to  absorption  by  air  of  its  own  radiation,  where  large  masses  are  involved,  as  in 
the  atmosphere. 

The  region  of  the  spectrum  in  which  the  radiation  of  air  lies,  may  possibly  be  inferred  from  the 
following  facts:  A  region  of  powerful  oxygen  absorption  exists  in  the  ultraviolet,  to  which,  in  all 
probability,  a  strong  baud  of  emission  corresponds ;  but  it  is  not  likely  that  any  emission,  produced 
by  simple  heating,  can  be  felt  in  this  part  of  the  spectrum  at  low  temperatures.  The  linear 
oxygen  absorption  groups — A,/>,  and  a — in  the  red,  and  a  series  of  faint  diffuse  bauds,  of  which 
the  strongest  corresponds  with  Brewster's  telluric  band  6  (A  =  0.565//  to  0.585yu)  in  the  yellow, 
together  with  any  others  of  a  like  order  which  await  identification  in  the  infra-red,  are  too 
insignificant  to  have  emission  counterparts  which  will  account  for  any  appreciable  fraction  of  the 
low-temperature  radiation  of  this  gas.  Nitrogen  and  argon  are,  so  far  as  we  now  know,  of  still 
less  importance,  since  no  telluric  bands  have  as  yet  been  traced  to  their  presence  in  the 
atmosphere. 

Two  facts  remain  to  be  considered.  Hutchins  found  that  a  plate  of  quartz,  0.5  cm.  thick, 
reduced  the  deflection  from  hot  air  from  151  div.  to  zero;  and  it  has  been  noted  (ante  p.  34)  that 
0.315  cm.  of  glass  appeared  to  transmit  8  per  cent,  of  air-radiation.  Besides  the  region  of  quartz- 
absorption  at  0.103/^,  H.  Kubeus  and  E.  F.  Nichols  (Phys.  Rev.,  vol.  5,  p.  105,  Aug.,  1897)  have  found 
bauds  of  metallic  reflection  and  total  absorption  for  this  substance  at  8.50 //,  9.02yw,  and  20.75//. 
The  first  two  of  these  bands,  with  the  neighboring  region  from  8/1  to  9.5^  through  which  trans- 
mission by  a  layer  of  quartz,  so  thin  as  18  u,  does  not  exceed  10  per  cent.  (Nichols,  Phys.  Rev.,  vol. 
4,  p.  307,  189?),  can  not  cover  the  atmospheric  bauds  which  we  are  seeking,  since  in  this  part  of 


113 


the  spectrum  solar  rays  pass  through  the  atmosphere  easily,  and  the  principal  emission  of  radiation 
from  hot  aqueous  vapor,  between  5yu  and  8  7,  also  lies  outside  of  this  region.  Hence  it  is  perhaps 
permissible  to  infer  that  the  low-temperature  emission  of  air,  which  is  so  completely  absorbed 
by  quartz,  has  a  wave-length  not  far  from  20.75A/,  and  that  air  also  absorbs  strongly  in  this 
region;  but,  if  so,  the  ratio  of  air- radiation  to  the  radiation  of  carbon  dioxide  ought  to  diminish 
as  the  temperature  rises,  at  least  until  those  very  high  temperatures  are  attained  which  favor  the 
emission  of  the  ultra-violet  band  of  oxygen,  and  there  is  no  evidence  of  this.  I  am  not  disposed 

•  OOQ 


50      60      10       80 

S^ig.  20 

•r 


30     100     HO     ttO   c-m. 


to  insist  upon  my  observation  of  a  feeble  transmission  of  radiation  from  air  by  glass,  because 
it  rests  upon  a  very  small  deflection,  but,  if  genuine,  it  indicates  a  discontinuity  and  essential 
difference  in  the  absorptions  by  glass  and  quartz  at  this  extreme  wave-length. 

GENERAL  APPLICATION  OF   THE  PRECEDING    STUDIES  OF  ABSORPTION  AND   RADIATION 
TO  THE  PROBLEMS  OF  ATMOSPHERIC  RADIATION. 

We  have  seen  that  a  highly  absorbent  gas,  and  one  which  is  also  an  equally  powerful  radiant 

in  thin  layers,  may  have  little  more  radiative  power  than  a  bad  radiator  when  the  depths  are 

greater,  the  positions  of  the  two  being  finally  reversed  at  still  greater  depths,  as  indicated  by  the 

extended  curves  of  fig.  20,  and  that,  in  fact,  there  is  not  as  much  difference  as  might  be  imagined 

12812—  Bull.  G  -  8 


114 

between  the  radiation  of  the  different  constituents  of  the  atmosphere  at  ordinary  temperatures 
and  when  in  large  masses.  The  facility  with  which  a  highly  radiative  vapor  parts  with  its  heat 
is  largely  annulled  by  self-absorption  of  its  own  radiations  in  deep  layers,  and  since  in  gases  heat 
is  transferred  from  molecule  to  molecule  with  the  greatest  ease,  it  is  probably  a  fact  that  small 
masses  of  mixed  gases  or  vapors,  such  as  are  used  in  laboratory  experiments,  radiate  chiefly  by 
their  most  highly  radiative  molecules,  the  others  transferring  their  heat  to  these  kinetically;*  but 
in  such  great  masses  as  are  concerned  in  atmospheric  thermal  and  radiant  processes,  it  is  the 
feebly  radiative  molecules  which  act  as  radiators,  except  in  a  comparatively  thin  outer  layer. 

While  laboratory  experiments  are  necessary  for  a  correct  understanding  of  the  processes 
which  go  on  in  the  simplest  cases  of  gaseous  radiation  and  absorption,  actual  quantitative  values 
which  may  be  of  use  in  large-scale  meteorological  computations  will  probably  still  have  to  be 
derived  by  meteorological  methods. 

There  seems  to  be  some  analogy  between  the  radiant  powers  of  dry  air  and  rock-salt.  Both, 
if  the  suggestion  on  page  113  be  accepted,  emit  ether- waves  ot  very  great  length.  Both  are  highly 
transmissive  in  that  part  of  the  spectrum  where  fall  the  emissions  from  bodies  at  ordinary  tempera- 
tures. In  small  masses  they  are  very  bad  radiators,  but  their  relative  radiant  efficiency  increases 
with  the  depth  of  the  radiant  layer. 

The  powerfully  radiant  vapors,  such  as  ammonia,  like  the  metals  among  solids,  radiate  from 
a  very  feeble  depth.  In  the  spectral  region  of  their  principal  emission,  after  exceeding  this  depth, 
no  further  increase  is  to  be  expected,  even  though  the  radiant  layer  be  increased  to  infinity;  and 
as  the  radiations  of  these  vapors  are  limited  to  definite  spectral  regions,  the  total  emission  must 
finally  exhibit  an  equally  definite  relation  to  that  of  a  black  body,  depending  upon  the  position 
and  extent  of  those  parts  of  the  spectrum  within  which  the  vapor  is  a  perfect  radiator.  In  like 
manner,  a  gas  which  is  very  feebly  absorbent  or  radiant  in  thin  layers,  has  some  depth  of  maximum 
efficiency  at  which  its  peculiar  bands  attain  the  greatest  possible  development.  If  these  bands, 
while  feeble,  are  wider,  or  occupy  more  extensive  regions  of  the  spectrum  than  those  of  the  strongly 
radiant  vapor,  and  are  of  such  wave-lengths  as  to  be  emitted  with  equal  readiness  at  the  given 
temperature,  the  gas  in  a  layer  of  great  depth  may  surpass  a  like  depth  of  vapor  as  a  radiator, 
although,  when  in  thin  layers,  the  vaporous  radiation  immensely  exceeds  the  gaseous.  Again,  if 
the  emission  bands  of  the  gas  are  more  numerous,  and  occupy  very  extensive  regions  of  the 
spectrum,  while  those  which  can  be  emitted  by  the  vapor  at  the  same  temperature  are  of  small 
extent,  a  layer  of  the  gas  less  than  the  depth  of  maximum  efficiency  (except,  perhaps,  at  some 
temperature  which  especially  favors  the  vapor's  emission)  may  radiate  better  than  the  vapor,  the 
feebleness  of  the  gaseous  emission-bands  being  compensated  by  their  great  number  or  wide  range 
through  the  spectrum.  The  rate  of  increase  of  radiation  with  temperature-elevation  will  depend 
also  upon  the  region  of  the  spectrum  to  which  the  emission  is  confined,  long  waves  increasing  in 
strength  more  slowly  than  short  waves. 

The  discrepancies  between  the  results  of  different  observers  of  gaseous  radiation,  working 
under  various  conditions  of  depth,  temperature,  etc.,  after  the  elimination  of  errors  involved  in 
methods  of  observation,  are  capable  of  being  reconciled,  and  seem  to  demand  varieties  of  spectral 
structure,  such  as  those  which  have  been  mentioned,  for  their  explanation.  To  apply  the  argu- 
ment to  the  components  of  the  atmosphere:  Carbon  dioxide,  so  far  as  is  now  known,  has  only 
three  emission-bands  in  the  infra-red.  Within  narrow  spectral  limits,  the  radiation  of  this  gas  is 
very  powerful,  requiring  only  about  a  meter-layer  to  give  maximum  efficiency.  The  almost  equally 
slow  increase  of  air-radiation  with  rise  of  temperature  is  perhaps  due  to  the  long  wave-lengths  of 
its  bauds;  but  the  very  gradual  growth  of  its  radiation  as  the  depth  enlarges  is  best  explained  by 
the  supposition  of  an  extensive  spectral  region  filled  with  numerous  feeble  emission-bauds  which 
grow  in  strength  very  slowly  as  the  depth  increases,  but  which,  nevertheless,  in  their  sum  total, 
eventually  surpass  the  radiation  of  the  few  strong  bauds  of  carbon  dioxide.  Whether  oxygen, 
nitrogen,  or  argon  are  concerned  in  this  primarily  feeble  einis&ioii  can  not  be  stated.  In  a  different 
category  from  either  of  the  other  atmospheric  constituents,  is  water-vapor.  Its  spectrum,  consists 
of  many  bauds  composed  of  very  numerous  fine  lines.  Some  of  these  bands  are  strong,  reaching 
maximum  development  with  a  slight  depth,  while  others  grow  slowly.  The  extent  of  spectrum 

*  See  Tyudall's  experiments  in  "varnishing"  air  molecules  with  those  of  more  powerfully  radiant  vapors. 


115 

filled  with  these  groups  is  very  great,  and  thus  the  radiation  is  large  with  a  small  thickness  of 
vapor,  and  yet  continues  to  increase  through  a  wide  range  of  depths.  The  importance  of  aqueous 
vapor  as  a  radiator  is  therefore  great ;  nevertheless,  in  layers  of  atmospheric  dimensions,  there  may 
not  be  as  much  difference  in  the  relative  efficiency  of  atmospheric  constituents  as  might  at  first 
appear.  Throughout  the  greater  part  of  this  vast  aerial  envelope  the  gaseous  molecules  can  not 
radiate,  except  so  far  as  the  stronger  radiators  emit  to  the  weaker,  and  these  to  the  outer  world. 
The  different  sorts  are  quite  independent  of  each  other,  but  those  of  a  kind  are  hemmed  in  by 
other  molecules  of  the  same  absorbent  properties  which  cry  "no  thoroughfare"  to  ether- waves 
which  have  their  own  vibratory  period.  Thus  it  is  that,  in  the  upper  air,  temperature  remains 
almost  constant  through  day  and  night,  and  only  changes  as  the  vertical  circulation  of  storms,  and 
the  general  movement  of  the  entire  atmosphere  from  equator  to  poles  and  back,  replaces  the  air 
at  any  given  level  and  terrestrial  position  by  other  air  which  has  acquired  its  temperature  else- 
where under  freer  conditions.  Only  at  the  borders  of  its  domain  is  any  constituent  of  the  air 
entirely  free  to  change  its  temperature  by  its  own  radiation. 

An  important  relation  results  from  the  facts  embodied  in  the  theory  of  a  maximum  radiant 
depth  in  a  gas,  when  combined  with  the  further  knowledge  that  this  depth  is  reached  at  different 
distances  for  particular  wave-lengths,  and  is  quickly  attained  for  those  rays  which  lie  near  the 
maximum  of  an  emission-band.  It  seems  permissible  to  say  already  that  so  far  as  gaseous  radia- 
tion depends  upon  simple  heating  of  the  gas,  the  ordinates  of  the  maxima  in  bands  of  different 
wave-length  (the  depth  being  sufficient  to  give  maximum;  radiant  efficiency  for  these  special  rays) 
are  related  to  each  other  in  the  same  way  as  are  the  ordinates  in  the  spectral  energy-curve  of  a 
black  solid  body.  As  the  temperature  rises,  the  heights  of  the  emission-bands  of  short  wave- 
length increase  more  rapidly  than  those  corresponding  to  the  longer  waves,  and  with  the  limita- 
tion noted  as  to  manner  of  excitation,  bands  at  the  shortest  wave-lengths  only  become  sensible  at 
those  high  temperatures  at  which  similar  radiations  first  appear  in  the  spectrum  of  a  black  solid. 
Not  only  is  this  relative  agreement  maintained,  but  the  absolute  energies  in  the  spectrum  at  a 
gaseous  band-center  and  at  the  same  point  in  the  spectrum  of  lampblack  for  the  same  tempera- 
ture are  almost  identical,  any  slight  inferiority  of  the  gaseous  radiation  being  probably  attributa- 
ble to  the  linear  constitution  of  the  band  and  the  absence  of  the  condition  of  maximum  efficient 
depth  for  some  of  the  rays  of  the  complex  bundle.  This  point  has  been  established  for  aqueous 
vapor  and  carbon  dioxide  by  the  observations  of  Pascheu  on  the  emission  of  heated  gases.  After 
noticing  facts  brought  forward  by  Pringsheim,  among  others  that  thin  wires  are. only  heated  to 
about  150°  C.  by  certain  flames,  such  as  that  of  carbon  bisulphide,  "  which,  notwithstanding,  send 
out  an  abundant  and  absolutely  blue  light,"  and  commenting  that,  in  spite  of  the  low  temperature 
of  the  wires,  "the  luminous  molecules  may,  nevertheless,  have  a  very  high  temperature"— a  con- 
clusion which  has  also  been  reached  by  Smithells  on  theoretical  grounds — Paschen  demonstrates 
experimentally  that,  whatever  part  chemical  action  may  have  in  originating  high  temperatures, 
the  vapor  of  water  and  carbon  dioxide  whose  discontinuous  emissions  make  up  the  chief  part  of 
the  spectrum  from  a  Bunsen-burner  flame,  radiate  solely  by  virtue  of  their  heat,  however  imparted. 
The  emission-bands  discovered  by  Julius  in  flame-spectra  were  reproduced  by  Paschen  by  simply 
heating  the  gases  without  any  combustion  whatever.  The  emission-bands  of  carbon  dioxide  were 
"  still  certainly  perceptible"  with  the  gas  at  73°  C.,  at  which  temperature  there  can  be  no  question 
of  dissociation  or  of  chemical  action ;  and  the  emission  from  aqueous  vapor  was  followed  to  280°  C. 
The  maximum  of  CO2  radiation  at  wave-length  4.3 /<,  exhibited  the  following  intensities  at  the 
given  temperatures:  At  842°  C.,  5G6  div.;  at  707°  C.,  357  div.;  at  450°  C.,  114  div.;  at  306°  C.,  37 
div.j  at  204.5°  C.,  11.1  div.;  at  165°  C.,  6.6  div.;  at  114°  C.,  3.0  div.;  and  the  highest  maximum  of 
water-vapor  at  wave-length  2.7  j.i  gave":  At  900°  C.,  146  div. ;  at  638°  C.,  25.4  div. ;  at  496°  C.,  5.6 
div. ;  at  400°  C.,  2.1  div. ;  at  284°  C.,  0.6  div.  ( Wied.  Ann.,  Bd.  50,  S.  428,  429,  1893.) 

Here  radiation  has  increased  with  temperature  at  a  more  rapid  rate  for  water  than  for  carbon 
dioxide,  or  in  accordance  with  the  usual  law  for  continuous  spectra  where  the  shorter  waves  have 
a  more  rapid  rate  of  increase  of  energy  than  the  longer ;  but  the  relation  between  the  intensities 
of  maxima  in  different  parts  of  the  spectrum  is  not  given  by  these  experiments,  since  the  maxima 
compared  do  not  belong  to  the  same  substance,  nor  can  it  be  a  definite  one  even  for  a  single 
radiator  unless  the  depths  exceed  maximum  efficiency  for  every  one  of  the  bands. 


116 

In  the  spectrum  of  steam,  7  cm.  deep,  at  500°  C.,  the  heights  of  the  long- waved  maxima  are 
nearly  equal  to  the  corresponding  ordinates  in  the  spectral  energy-curve  of  lampblack  at  the  same 
temperature.  At  wave-length  5.6;.-,  "where  the  water- vapor  spectrum  has  the  intensity  87  mm., 
lampblack  at  500°,  under  like  conditions,  gives  a  galvanometer  deflection  of  about  110  mm."  At 
6.O//  "these  intensities  are  for  water  G6,  for  lampblack  about  80,"  but  at  2.7 j.i  "on  the  other  hand, 
for  water  139,  for  lampblack  320  mm.,"  showing  that  the  depth  of  7  cm.  is  insufficient  to  fully 
develop  the  radiation  of  the  last-named  band.  ( Wied.  Ann.,  Bd.  51,  S.  3G,  1894.)  The  height  of  the 
emission- maximum  at  2.7 /.i  was  increased  from  20  mm.  to  139  mm.  when  the  depth  was  increased 
from  3  mm.  to  70  mm.  (Loc.  cit.,  p.  35.) 

The  changes  in  the  spectral  energy-curve  of  radiant  aqueous  vapor  produced  by  variations  of 
temperature  are  still  more  marked  than  those  from  varying  depth.  Thus  while  the  aqueous 
absorption  is  most  intense  in  the  long-waved  bands,  and  while  these  bands  are  also  most  promi- 
nent in  the  emission  at  low  temperatures,  the  band  at  2.7/t  has  a  height  twenty  times  as  great  as 
the  former  in  the  spectrum  of  the  oxyhydrogen  flame.  Hence  different  bands  in  the  spectrum  of 
the  same  substance  follow  different  laws  of  increment,  both  as  to  temperature  and  as  to  depth. 

Carbon  dioxide  at  wave-leugth  4.3;-,  in  even  so  small  a  depth  as  7  cm.,  behaves  very  much  like 
a  black  body,  both  as  regards  the  absolute  intensity  of  its  radiation  and  its  variation  with  the 
temperature.  Paschen's  curve  for  the  latter  quantity  (Wied.  Arn.,  Bd.  51,  Taf.  1,  fig.  9)  falls  but 
little  below  the  corresponding  curve  for  lampblack,  indicating  that  7  cm.  is  very  near  the  maximum 
efficient  depth  for  certain  rays  from  this  gas. 

It  is  not  to  be  expected  that  a  vapor  which  is  quite  colorless  and  transparent  for  luminous 
rays  should  give  a  continuous  visible  spectrum  even  when  highly  heated;  but  the  same  gas  in 
another  part  of  the  spectrum  may  have  its  vibrations  damped  through  a  wide  range  of  wave-length, 
provided  the  depth  or  density  of  the  radiant  layer  be  sufficient.  The  wide  bands  thus  produced 
resemble  those  limited  spectral  regions  within  which  certain  phosphorescent  solids  and  liquids 
radiate  exclusively,  but  without  giving  definite  line-spectra. 

Strongly  colored  gases  which  absorb  visible  rays  emit  continuously  in  the  same  visible  region 
of  the  spectrum.  Mr.  J.  Evershed's  experiments  on  the  radiation  of  heated  gases  (Phil.  Mag.  (5), 
vol.  39,  p.  465, 1895)  prove  "that  besides  iodine,  the  vapors  of  bromine,  chlorine,  sulphur,  selenium", 
and  arsenic  can  all  be  made  more  or  less  incandescent  by  heating  to  the  temperature  at  which 
glass  combustion-tube  softens,  and  the  light  emitted  by  each  of  these  glowing  vapors  appears  to 
give  a  perfectly  continuous  spectrum,  while  the  corresponding  absorption-spectra  are  selective. 
Thus  there  is  no  such  close  relation  between  emission  and  absorption  as  is  implied  by  Kirchoff's 
law  of  radiating  bodies.  There  seems,  however,  to  be  a  general  relation  between  the  total  absorbing 
and  radiating  power  for  the  visible  rays." 

The  production  of  those  distinct  and  widely  separated  vibrations  which  give  line-spectra, 
demands  considerable  freedom  of  motion,  such  as  exists  in  the  partial  vacuum  of  a  Geissler's  tube, 
in  the  high  dilution  of  minute  traces  of  metallic  salts  distributed  through  the  mass  of  a  Buusen 
flame,  or  in  the  very  thin  surface  layers  at  the  inner  and  outer  surfaces  of  such  a  flame,  where 
chemical  action  is  going  on.  Spectral  differences  are  also  found  at  different  flame-levels,  testifying 
to  a  succession  of  chemical  interchanges  which  undoubtedly  favor  the  production  of  line-spectra. 
Thus,  cupric  chloride  in  the  Bunsen  flame  gives  successive  sheaths  of  yellow,  red,  blue,  and  green 
flame,  due  to  metallic  copper,  cuprous  chloride,  and  cuprous  oxide,  as  Professor  Sinithells  has 
shown  by  means  of  his  cone-separator  for  studying  the  flame  of  the  Bunsen  burner.  (Phil.  Mag.  (5), 
vol.  39,  p.  122,  1895.)  Very  brilliant  spectra  of  the  copper  salts  may  be  obtained  by  means  of  a 
copper  wire  which  has  stood  for  some  time  in  hydrochloric  acid,  and  has  become  deeply  corroded. 
There  is  also  in  this  case  a  partial  separation  of  the  flame-effects  as  successive  layers  of  the  corroded 
film  burn  off. 

The  mechanism  by  which  the  discontinuous  radiations  of  the  electric  glow  in  rarefied  gases 
and  of  flames  are  produced  has  been  the  subject  of  much  speculation.  Werner  Siemens,  in  1882, 
wrote : 

If  we  assume  that  the  gas-molecules  are  surrounded  by  a  sheath  of  ether,  an  alteration  of  these  sheaths  of 
ether  must  take  place  whon  two  or  more  such  molecules  combine  chemically.  The  resultant  movement  of  the  ether- 
particles  must  be  compensated  by  vibrations  which  may  form  the  starting  point  of  the  outflow  of  waves  of  light 


117 

and  radiant  heat.     In  quite  a  similar  way  we  can  picture  the  light-effects  which  appear  when  an  electric  current  is 
passed  through  gases.     ( Wied.  Ann.  Bd.  18,  S.  315.) 

Since  the  current  conducted  by  gas  appears  to  be  always  accompanied  by  chemical  action,  the  glow  might  be 
explained  as  in  llarnes  through  the  oscillating  environment  of  the  etherial  sheaths  of  the  gaseous  molecules  by 
which  the  passage  of  the  electricity  will  be  facilitated.  (Loc.  cit.,  p.  316.) 

Others  have  imagined  the  gaseous  molecule  to  consist  of  a  congeries  of  atoms  whose  configura- 
tion being  changed  by  electrification,  or  during  the  act  of  chemical  combination,  for  example, 
certain  of  the  atoms  being  temporarily  separated  from  their  groups,  or  ionized,  there  results  a 
series  of  atomic  oscillations  about  a  mean  position,  until  the  energy  of  the  disturbance  is  dissi- 
pated as  radiant  energy  of  similar  periods.  As  thus  stated,  this  hypothesis  offers  no  suggestion 
of  the  mode  by  which  energy  is  transferred  from  the  atoms  to  the  ether.  But  if  the  gaseous  mole- 
cule is  composed  of  linked  atomic  vortices  of  ether,  or  of  associated  concentric  vortices,  in  which 
are  critical  or  limiting  surfaces,  conditioned  by  changes  of  form  or  velocity  of  etherial  movement, 
the  rearrangement  of  these  groups  determined  by  chemical  interchange,  or  their  disturbance  from 
positions  of  equilibrium  by  electrification,  may  engender  waves  in  the  critical  surfaces  whose 
periods  depend  upon  the  dimensions  and  surface- velocities  of  these  loci.  The  passage  of  systems 
of  waves  over  such  closed  surfaces  may  give  foci  of  interference,  and  it  is  possible  that  the  con- 
nection and  order  observed  in  the  frequencies  of  the  numerous  sorts  of  vibrations  which  the  atoms 
of  one  element  can  execute  simultaneously,  or  at  least  in  such  rapid  recurrent  succession  that  the 
series  can  not  be  distinguished  from  a  simultaneous  one,  are  to  be  thus  interpreted. 

The  hypothesis  of  Arrhenius  which  assumes  ionization  of  a  gas  wherever  line-spectra  are 
produced,  demands  a  certain  amount  of  ionic  dissociation  even  at  comparatively  low  temperatures, 
and  this  has  perhaps  not  been  demonstrated  except  under  peculiar  conditions  of  electrification; 
but  whether,  for  example,  we  conclude  as  Liveing  and  Dewar  did  (Proc.  Roy.  Soc.  London,  vol. 
30,  p.  152,  1880;  see  also  vol.  34,  p.  418, 1882,  where  somewhat  conflicting  testimony  is  given),  that 
the  bands  in  the  spectrum  of  the  blue  base  of  a  Buiisen  flame  are  due  to  carbon  and  hydrogen  in 
the  act  of  uniting  or  separating,  in  the  formation  or  destruction  of  acetylene,  the  chemical  union 
of  these  two  substances  being  considered  essential  to  the  exhibition  of  this  spectrum,  or  whether, 
with  Lockyer  and  others,  the  spectrum  in  question  be  attributed  to  carbon  vapor  alone,  I  think 
we  must  agree  with  Arrhenius  that  it  is  an  atomic  rather  than  a  molecular  motion  which  produces 
the  line-spectrum,  and,  in  general,  it  is  molecular  motion  which  gives  extensive  diffuse  bauds, 
such  as  those  of  the  absorption-spectra  of  liquids,  and  the  absorption  and  emission  spectra  of 
some  gases. 

Is  it  necessary,  however,  that  atoms  should  be  completely  free  in  order  that  their  vibrations 
may  give  line-spectra?  A  distinction  between  the  spectra  of  free  and  of  partially  constrained 
atoms  may  be  granted,  but  it  seems  permissible  to  assume  that  some  of  the  most  persistent  vibra- 
tions may  be  emitted  by  atoms  in  the  midst  of  their  aggregations  which  constitute  the  molecules. 
Prof.  A.  A.  Michelson  ("On  the  broadening  of  spectral  lines,"  Astroph.  Journ.,  vol.  2,  p.  251,  Nov., 
1895)  finds  that  rarefied  hydrogen  (pressure  about  1  mm.)  gives  out  its  characteristic  spectrum 
under  the  action  of  an  electric  discharge  at  a  remarkably  low  temperature.  The  width  of  a  line 
having  been  proved  to  increase  as  the  temperature  rises  in  the  ratio  of  the  square  roots  of  the 
absolute  temperatures,  the  width  of  the  red  hydrogen  line  in  an  uuheated  tube  was  found  to 
correspond  to  a  temperature  not  more  than  50°  C.  above  the  surroundings,  or  320°  absolute.  The 
emission  of  visible  radiations  at  such  a  low  temperature  implies  that  the  rays  are  not  produced 
by  simple  heating  (molecular  motion  or  rectilinear  motion  of  free  ions),  but  that  the  passage  of  the 
electric  spark  by  ionic  motions  increases  the  motions  (either  rotations  or  oscillations)  within  the 
molecules,  modifying  the  internal  atomic  motions  without  changing  the  rectilinear  velocities  of  the 
atomic  aggregates  to  any  great  extent.  On  the  contrary,  since  hydrogen  and  other  simple  gases 
may  be  heated  to  very  high  temperatures  without  causing  them  to  emit  visible  radiations,  it  is 
evident  that  the  shocks  produced  by  external  collisions,  due  to  rectilinear  motions,  are  not  as 
efficacious  in  setting  up  internal  atomic  vibrations  as  are  the  torsions  experieiK  ed  during  the 
passage  of  a  spark.  The  aurora  is  a  case  in  point.  In  the  middle  latitudes  it  occurs  usually  at 
heights  exceeding  40  miles,  where  the  air  is  intensely  cold,  and  is  an  instance  of  visible  atmos- 
pheric radiation  produced,  not  by  direct  thermal  means,  but  electrically. 


118 

ATMOSPHERIC   DUST. 

The  experiments  with  dust-laden  air  have  indicated  that  the  addition  of  a  small  amount  of 
solid  matter,  diffused  through  a  large  volume  of  air,  does  not  change  the  radiating  power  of  the 
latter  perceptibly.  The  same  conclusion  may  be  drawn  from  the  use  of  smoke  to  prevent  frost,  for 
if  the  finely  divided  carbon  increased  the  radiating  power  of  the  air,  the  protection  would  be  less 
effectual.  The  principal  result  which  can  be  traced  to  the  presence  of  floating  dust  is  its  modifica- 
tion of  atmospheric  transmission  by  the  reflection  and  scattering  of  rays  during  their  passage 
through  the  turbid  medium. 

Tyndall  imitated  the  blue  color  of  the  sky,  and  even  the  peculiar  polarization  of  its  light — 
which  is  a  maximum  90°  from  the  sun,  and  which  exhibits  neutral  points  where  the  plane  of 
polarization  changes — by  precipitating  a  mist  of  attenuated  solid  or  liquid  particles,  of  scarcely 
more  than  molecular  dimensions,  from  mixed  rarefied  vapors  capable  of  reacting  chemically  under 
the  influence  of  light.  By  choosing  substances,  "  one  at  least  of  whose  products  of  decomposition 
under  light  shall  have  a  boiling  point  so  high  that  as  soon  as  the  substance  is  formed  it  shall  be 
precipitated,'1''  solid  or  liquid  particles  of  great  fineness  are  produced  without  having  time  to  cohere 
into  coarser  agglomerates.  "  By  graduating  the  quantity  of  the  vapor  this  precipitation  may  be 
rendered  of  any  degree  of  fineness,  forming  particles  distinguishable  by  the  naked  eye,  or  particles 
which  are  far  beyond  the  reach  of  our  highest  microscopic  powers."  (Contributions  to  Molecular 
Physics,  p.  431,  from  Proc.  Roy.  Soc.  London,  No.  108,  1869.) 

As  the  particles  become  coarser  they  cease  to  reflect  selectively,  at  least  in  the  visible  spec- 
trum, but  return  light  of  every  refrangibility  in  nearly  equal  proportion.  In  this  way  a  cirro- 
stratus  cloud  spreads  white  light  all  over  the  sky,  overpowering  the  blue  light.  In  like  manner  a 
fog,  dense  enough  to  obscure  the  rays  of  the  sun,  may  diffuse  enough  of  sunlight  to  produce  quite 
a  bright  general  illumination;  but  in  this  case  the  reflection  is  not  absolutely  devoid  of  selective 
properties.  To  the  palm  of  the  hand  held  up,  the  position  of  the  un.seen  sun  is  revealed  through 
the  sensation  of  warmth  produced  by  solar  rays  of  great  wave  length  which  are  capable  of  pene- 
trating the  mist.  The  obscure  rays  may  also  be  recorded  by  the  actinoineter,  and  analyzed  by  the 
spectroboloineter,  which  shows  that  a  mist,  capable  of  keeping  out  all  of  the  visible  rays  in  the 
direct  beam,  may  still  transmit  infra-red  waves  beyond  2/<  rather  freely. 

Lord  Eayleigh  (Phil.  Mag.  (5),  vol.  47,  p.  375,  1899)  finds  that  diffraction  from  the  molecules  of 
the  air,  which  are  of  small  dimensions  relatively  to  the  waves  of  light,  is  competent  to  account  for 
a  large  part  of  the  selective  scattering  of  short  waves  in  sky  light,  and  for  the  actual  transmission 
of  the  visible  part  of  the  spectrum.  If  .r  is  the  distance  through  which  light  must  pass  in  air  at 
atmospheric  pressure  before  its  intensity  is  reduced  in  the  ratio  of  the  basis  of  natural  logarithms 
to  unity, 

*=32,f(;% 

where  n  is  the  number  of  molecules  in  the  unit  of  volume,  or  19  x  (10) 18  per  cubic  centimeter 
according  to  Maxwell,  /<  is  the  refractive  index  as  modified  by  the  spherical  molecules,  j.i  —  1  =  .0003, 
and  A  is  the  wave-length  of  light.  Taking  Bouguer's  estimate  of  the  transmission  of  star-light  by 
an  entire  atmosphere,  namely  0.8,  we  find,  since  the  maximum  sensitiveness  of  the  eye  for  light  as 
faint  as  that  of  the  stars  is  about  at  wave-length 

A  =  5  x  (10) -5  cm., 
x  =  40  kilometers. 

The  homogeneous  atmosphere  being  8.3  kilometers  thick,  the  observed  transmission  by  40  kilo- 
meters is : 


r\  40-° 
0.8  )  M  =  0.34 


which  does  not  differ  much  from  the  assumed  transmission,    =  0.37. 

'  e 

If  Bouguer's  eye  was  most  sensitive  to  yellow  rays  at  A  =  C  x  (10)—  5  cm.,  x  =  83  kilometers, 
and  the  corresponding  observed  transmission,  (0.8)  ln  =  0.11,  is  less  than  a  third  of  that  computed  by 


119 

the  hypothesis  of  molecular  diffraction,  leaving  a  considerable  part  of  the  blue  light  of  the  sky  to 
be  supplied  from  other  sources.  There  can  be  no  doubt,  however,  that  the  exponent  of  A  should  be 
larger  than  4  at  the  blue  end  of  the  spectrum,  and  smaller  than  4  in  the  infra-red,  as  Lord  Eayleigh 
suggests  (loc.  cit.,  p.  383).  The  formula,  as  it  stands,  gives  for  A  =  0.293yi<  a  transmission  by  one 
atmosphere  of  0.17,  and  for  A  =  1.0/t  a  transmission  of  0.99;  but  the  former  is  known  to  be  zero, 
and  the  latter,  as  far  as  it  depends  on  selective  scattering,  is  probably  more  nearly  equal  to 
0.91)  —  0.17  =  0.82.  The  sudden  termination  of  the  solar  spectrum  at  0.293;/  may  be  produced  by 
a  local  absorption-baud  of  oxygen,  but  selective  scattering  gives  nearly  the  same  limit. 

Coruu  (Comptes  rendus,  t.  88  and  89)  finds  that  the  limit  of  atmospheric  transmission  in  the 
ultra-violet  with  a  clear  sky,  depends  on  the  barometric  pressure,  thus  on  the  oxygen  and  nitrogen 
contents,  rather  than  on  aqueous  vapor  or  other  variable  constituent  of  the  air.  If  it  were  not 
for  this  fact  it  might  be  supposed  that  the  molecules  of  water-vapor,  or  the  products  of  condensa- 
tion resulting  from  the  continual  diffusion  of  a  very  rare  aqueous  vapor  into  the  upper  atmosphere, 
might  be  the  sole  cause  of  sky-color,  since,  as  Tyndall  remarks  (Heat  as  a  Mode  of  Motion,  p.  414), 
"the  color  of  the  firmamental  blue,  and  of  distant  hills,  deepens  with  the  amount  of  aqueous  vapor 
in  the  air,"  and  in  part  this  may  be  an  additional  cause  of  coloration,  although  it  appears  to  be  of 
no  importance  in  determining  the  limit  of  the  spectrum.  The  association  of  the  deepest  blue  sky 
with  the  descending  air  of  the  tropical  calms  may  be  explained  by  the  purification  which  the  air 
has  undergone.  The  coarser  dust  having  been  washed  out  in  the  abundant  precipitation  of  the 
equatorial  rains,  the  genuine  color  of  the  sky  resulting  from  molecular  diffraction  is  no  longer 
obscured  by  the  more  general  scattering  of  light  by  the  larger  and  unassorted  particles. 

The  beautifully  colored  coronas  and  patches  of  color  seen  upon  incipient  cirrus  near  the  sun 
are  due  to  diffraction  from  ice  or  water  particles  of  a  coarser  order  than  the  molecular,  and 
graduate  into  cases  of  simple  and  indiscriminate  reflection  from  still  coarser  particles,  an  effect 
which  becomes  very  great  at  large  angles  of  incidence,  and  produces  the  strong  glow  around 
the  sun,  never  absent  except  in  a  sky  of  exceptional  purity,  such  as  can  only  be  found  at  great 
altitudes. 

Whymper  in  his  Travels  Amongst  the  Great  Andes  of  the  Equator,  page  324,  thus  describes  the 
effect  of  clouds  of  volcanic  dust  from  Cotopaxi: 

When  they  commenced  to  intervene  between  the  sun  and  ourselves  the  effects  which  were  produced  were 
truly  amazing.  We  saw  a  green  sun,  and  smears  of  color  something  like  verdigris  green  high  up  in  the  sky,  which 
changed  to  equally  extreme  blood-reds,  or  to  coarse  brick-reds,  and  then  passed  in  an  instant  to  the  color  of  tarnished 
copper,  or  shining  brass.  No  words  can  convey  the  faintest  idea  of  the  impressive  appearance  of  these  strange 
colors  in  the  sky — seen  one  moment  and  gone  the  next — resembling  nothing  to  which  they  can  properly  be  compared, 
and  surpassing  in  vivid  intensity  the  wildest  effects  of  the  most  gorgeous  sunsets. 

I  think  there  can  be  no  doubt  that  these  vivid  colors  were  entirely  due  to  diffraction,  owing 
their  brilliancy  to  the  uniformity  in  the  size  of  the  particles  producing  them.  The  description 
reminds  one  of  the  colors  of  soap  bubbles  in  sunshine.  Cirrus  clouds  are  apt  to  be  composed 
of  ice  crystals  in  the  act  of  forming  from  vapor.  The  particles  are  constantly  growing  in  an 
irregular  way,  and  numerous  diffraction  rings  produced  by  means  of  swarms  of  particles  of  as 
many  different  diameters,  are  superimposed,  so  that  the  blended  colors  are  not  pure,  and  there  is 
much  white  light. 

In  general,  a  part  of  the  diminution  of  solar  rays  in  passing  through  the  air  is  due  to  selective 
scattering  by  air-molecules,  to  which  diffraction  by  ice-crystals  of  minute  size,  and  reflection  from 
dust  of  every  sort  may  be  added  in  a  hazy  atmosphere;  but  these  causes  have  very  little  influence 
upon  the  true  atmospheric  radiation  which  consists  chiefly  of  long  waves  but  little  affected  by  dust. 

SUMMARY. 

The  exposition  of  a  few  leading  principles  is  needed  to  give  entrance  and  guidance  in  a  general 
survey  of  the  subject.  Atmospheric  radiation  is  so  extensively  modified  by  atmospheric  absorption 
of  rays  that  the  subject  of  the  atmosphere's  transmissive  power  must  be  included. 

The  atmosphere  by  its  molecular  constitution  produces  a  selective  scattering  of  the  rays  which 
pass  through  it,  which  is  greatest  for  the  short  waves.  Ether-waves  of  greater  length  than  2^u 
•are  but  little  affected  by  selective  scattering,  but  throughout  the  visible  spectrum  there  is  an 


120 

increasing  depletion  of  the  direct  radiant  beam,  progressing  a  little  more  rapidly  than  the  inverse 
fourth  power  of  the  wave-length.  The  rays  taken  out  of  the  direct  beam  in  this  way  do  not  alter 
the  temperature  of  the  air,  and  a  large  part  of  them  reach  the  Earth's  surface.  The  same  is  the 
case  with  the  light  diffracted  by  minute  ice-crystals,  or  more  indiscriminately  reflected  by  coarser 
dust-particles. 

An  entirely  different  process  is  involved  in  the  production  of  local  line  and  band  absorption. 
Special  rays  are  absorbed  by  the  atoms  and  molecules  of  the  various  atmospheric  constituents. 
Here  the  energy  which  exists  in  the  ether  as  radiation  is  transformed  into  the  energy  of  molecular 
or  atomic  movement,  and  remains  in  the  atmosphere  as  an  increase  either  of  its  sensible  tempera- 
ture or  of  its  latent  heat.  The  ultra-violet  rays  appear  also  to  produce  chemical  change  in  some 
of  the  atmospheric  substances,  accompanied  by  electrification.  The  composition  of  the  atmosphere 
is  being  continually  changed  by  emanations  from  the  Earth  and  its  inhabitants,  and  the  atmospheric 
thermal  energy  is  increased  in  this  way,  and  especially  by  the  latent  heat  of  vaporization  of  water. 
Heat  is  also  developed  dynamically  whenever  there  are  descending  movements  in  the  air.  High 
winds  in  dry  and  dust-laden  air  generate  large  amounts  of  frictional  electricity,  and  a  part  of  this 
thermal  and  electrical  energy  imparted  to  the  air  from  many  sources,  is  eventually  given  out  again 
in  the  form  of  radiation. 

The  actual  spectral  energy-curve  of  a  depleted  sunbeam  is  a  complex  of  an  exceedingly  varie- 
gated original  radiant  energy,  as  further  modified  by  telluric  absorption,  every  one  of  whose  lines 
and  bands  has  a  separate  origin  and  law  of  variation.  In  like  manner  the  radiation  emitted  by 
the  air  is  made  up  of  a  great  variety  of  individual  lines  and  bands,  each  having  a  law  of  its  own, 
depending  on  the  pressure,  depth,  temperature,  and  physical  state  of  the  productive  constituent. 
In  a  measure  the  emission  by  the  air  resembles  its  absorption,  but  is  confined  to  the  longer  waves 
when  thermally  produced  at  relatively  low  temperatures.  Unknown  regions  in  which  the  oxygen, 
nitrogen,  argon,  and  krypton  of  the  atmosphere  radiate  at  low  temperatures,  remain  to  be  explored. 
The  chief  radiations  which  can  now  be  definitely  placed  in  the  spectrum  are  those  of  aqueous 
vapor  and  carbon  dioxide.  Owing  to  the  feebleness  of  these  radiant  bands  at  low  temperatures, 
the  positions  and  relative  intensities  of  the  more  refrangible  ones  are  best  studied  in  the  absorption- 
curve  of  the  solar  spectrum. 

The  following  table  (75)  of  positions  and  intensities  of  infra-red  bands  in  the  solar  spectrum 
has  been  compiled  from  two  plates — (a)  A  to  cj2,  (&)  (*>i  to  deviation  38°  45' — accompanying  an 
article  on  the  "Infra-red  solar  spectrum  of  a  60°  rock-salt  prism,"  published  in  the  Annual  Report 
of  the  Smithsonian  Institution  for  1897,  Appendix  Y,  pp.  66-68.  The  standard  temperature  of  the 
prism  is  stated  to  be  20°  C.  "The  positions  of  about  225  absorption  lines  and  bands  are  deter- 
mined *  *  *  between  deviations  of  40°  25'  and  38°  45',  corresponding  to  wave-lengths  0.76  u 
and  5.20 //,  respectively."  These  curves  are  the  culmination  of  Langley's  long  labors  in  the  solar 
spectrum.  No  band  is  included  in  the  present  list  which  is  not  also  shown  on  the  three  bolographs 
exhibited  by  Professor  Langley  at  the  Oxford  meeting  of  the  British  Association  (Astropliysical 
Journal,  vol.  1,  p.  162,  pi.  9,  Feb.,  1895).  The  numbers  assigned  here  to  the  intensity  of  absorption 
at  the  centers  of  the  individual  bands  have  been  obtained  by  comparing  the  bolographic  ordinates 
with  those  of  a  smooth  curve  passed  by  estimation  through  the  unabsorbed  maxima.  A  list  of 
these  maxima  and  their  intensities  in  the  prismatic  spectrum  follows: 

TABLE  74. 


Minimum  de- 
viation. 


40 
40 
39 
39 
39 
39 
39 


24.5 
9.0 
56.4 
47.0 
38.0 
28.5 
12.0 


Intensity  of 
radiation. 


11 
24 
38 
54 
63 
31 
18 


[14] 
[28] 
[45] 
[64] 
[77] 
[H2] 
[36] 


121 


The  numbers  in  brackets  are  the  values  obtained  by  correcting  for  atmospheric  absorption. 
The  adopted  curve  has  been  made  symmetrical  on  the  side  of  greater  wave-length  to  allow  for  the 
undoubtedly  very  large  absorption  of  the  entire  spectrum  as  the  great  bands  of  water- vapor  and. 
carbon  dioxide  are  approached,  since  in  this  region  the  intervening  points  of  comparatively  unab- 
sorbed  energy  begin  to  be  encroached  upon  by  the  bands.  The  corrected  values  have  been 
assigned  after  taking  account  of  the-extensive  stretch  of  almost  total  absorption  between  5  //  and 
8//,  and  the  probable  form  of  the  original  spectral  energy-curve  before  the  radiation  entered  the 
Earth's  atmosphere  has  been  inferred  by  supplying  these  missing  regions.  The  limits  adopted  for 
the  breadths  of  the  bands  and  groups  of  bauds  are  somewhat  arbitrary,  owing  to  the  very  gradual 
way  in  which  the  slopes  of  the  energy-curve  begin : 

TABLE  75. 


Designation  of  band.      ^HSTot 

Wave-length. 

Transmission.       Absorption. 

AVave-lengths  assigned 
by  other  observers. 

Source  and 
remarks. 

C              I 

/* 

Per  cent.           j     Per  cent. 

Great  A 

40    24.0 

0.76 

1-^-14.  2=  7.  0  i              93     Abney.                          Telluric. 

A, 

40    23.6 

0.77 

2—14.  5=13.  8                86 

Photography.   Dif-  \  Oxygen. 

fraction  grating. 

Brewster's  Yi 

40     16.  7  to 

0.82 

10^20.  6=48.  5                52 

.  816-.  821 

lucludes  so- 

15. 5 

lar  Na.  818. 

"          Y 

40     15.  3 

0.825 

8-21.  3=37.  6 

62                      .  823 

J3 

40    15.  0  to 

0.83 

9—22.  4=40.  2                50                      .  825-.  832 

13.5 

"          Ji              40    12.2 
"          X              40     11.7 

0.855 
0.86 

16-24.  6=65.  0 
15—25.  2=59.  5 

35                      .854 
40                      .866 

j  Solar  Ca. 

40    10.  5 

0.875 

20—26.  4=75.  8                24 

40      7.  7  to 

.  895-  .  91 

18-30.  0=60.  0                40                      .  895-.  903 

6.6 

Telluric, 

Abney's  n 

40      6.  6  to 

.  91  -  .  915 

18—30.  9=58.  3                42                      .  905-.  911 

probably 

6.0 

aqueous. 

40      6.  0  to 

.915-  .92 

18—31.  8=56.  6 

43 

.  912-.  918 

5.2 

Rbo-tau  group            40      4.  6  to 

0.  925  to 

Breadth, 

39    59.5 

0.985 

U.060/*. 

Abnev's  p                     40      4.  6  to 

.925-  .935 

6—33.  4=18.  0 

82 

.  930-.  939 

3.5 

"        6                    40      3.5  to 
1.  3 

.935-  .965 

8—35.  7=22.  4 

78 

.  943-.  950 

Telluric, 

"        r                    40      1.  3  to 

.965-  .985 

23—38.  4=59  9 

40 

probably 

39    59.  5 

aqueous. 

39    58.  7 

1.00 

32-^41.  4=77.  3 

23 

i     39    54.8 

1.06 

37—48.3=76.6                23 

Great  phi  group         39    53.  7  to 

1.085  to 

Breadth, 

39    47.0 

1.24 

0.155«. 

Abney's  #                    39    53.  7  to 

1.085  to 

9—52.  7=17.  1                83 

Telluric  wa- 

51.6 

1.125 

ter  vapor. 

39    51.  6  to 

1.  125-1.  13 

11—55.  0=20.  0 

80 

51.1 

39    51.1  to 

1.13  -1.16 

13-56.  9=22.  8 

77 

Includes  so- 

49.8 

lar  Na  1.132. 

39    49.  3 

1.17 

39—59.  4=65.  7 

34  ! 

39    48.5 

1.19 

43—60.  9=t70.  6 

29     Grating  and  spec-  i 

trobolometer. 

\i 

39    46.  5  to 

1.  IT.  -1.  28 

45-66.  0=68.  2 

32     Paschen. 

45.2 

Great  psi  group          39    45.  0  to 

1.  28  to 

Bunseu  flame,  1.33// 

Breadth, 

39    38.  2 

1.52 

to  1.50//. 

0.240//. 

39    43.7 

1.32 

29—70.  9=40.  9 

59 

Abney's  W 

39    43.  0  to 

1.  34  -1.  40 

4—73.  4=  5.  4 

95 

41.0 
39    40.8 

1.405 

8-75.  0=10.  7 

89 

Telluric 

39    39.9 

1.44 

16—76.  1=21.  0 

79 

water  va- 

39   37.5 

1.54 

58—76.  8=75.  5 

25 

por. 

39    36.8 

1.57 

58—76.  4=75.  9 

24 

39    36.1 

1.59 

58-75.9=76.4 

24 

Great  omega  group     39    34.  8  to 

1.  65  to 

Bunsenflame.l.75/<     Breadth, 

39    28.  5 

2.03 

to  2.10^.                       0.370w. 

Langley's  £1                39    33.  0  to 

1.  75  -1.  87 

1—66.4=  1.5 

99 

30.8 
"           co,                39    30.  3  to 
29.6 

1.  91  -1.  97 

9-65.  0=13.  8 

86 

Telluric 
water  va- 

"          GO.-               39    29.  6  to 

1.97  -2.03 

21-63.  0=33.  3 

67 

por. 

•28.  5 

122 

TABLE  75 — Continued. 


Designation  of  baud. 

Minimum  rock- 
salt  deviation. 

Wave-length. 

Transmission. 

Absorption. 

Wave-lengths  assigned 
by  other  observers. 

Source  and 
remarks. 

o          / 

n 

Per  cent. 

Per  cent. 

Great  chi  group 

39    28.  0  to 

2.  08  to 

Bunsen  flame,2.42/i 

Breadth, 

39     11.  5 

3.48 

to  3.02/u. 

1.400//. 

Langley's  JT 

39    23.  7  to 

2.  36  -9.  86 

1_49.  0=  2.  0 

98 

H(~\    i    f~1f\ 
•*  \J  "+•  V-<  V/->  • 

17.9 

Xi 

39    17.2 

2.92 

3-43.  5=  6.  9 

93 

39     16.  4 

2.99 

3-42.  5=  7.  1 

93 

39     15.  9 

3.02 

9—41.  7=21.  6 

78 

X-2 

39    15.0 

3.10 

:!-40.  3=-  7.  4 

93 

39     14.  3 

3.15 

5—39  3=12.  7 

87 

39    13.  8 

3.20 

4—38.  6=10.  4 

90 

39     13.  2 

3.24 

7-37.  8=18.  5 

82 

39    12.6 

3.29 

12-36.  8=32.  6 

67 

Telluric 

39    11.  3  to 

3.41  -3.46 

14—34.  5=40.  6 

59 

water  va- 

10.7 

por. 

39     10.  7  to 

3.  46  -3.  53 

14-33.  3=42.  0 

58 

9.6 

39      9.1 

3.58 

11-31.  8=34.  6 

65 

39      7.  0  to 

3.  73  -3.  80 

9-29.  0=31.  0 

69 

6.3 

39      6.  3  to 

3.  80  -3.  87 

9—28.  2=31.  9 

68 

5.  5 

Great    upsilon 

/  39      5.5  to 
1   38    55.0 

3.  87  to 
4.60 

Grating  and  spec- 
trobolometer, 

Breadth, 

0.730//,  tel- 

group 

f  39      2.  0  to 

4.  12  to 

l-f-21.  4=  4.  7 

95 

Paschen.  Bunsen 

luric  carbon 

2^ 

|  38    56.5 

4.43 

flame,4.15//-4.39//. 

dioxide. 

The  great  bands  of  which  the  radiation  of  the  atmosphere  at  slight  excess  of  temperature 
mainly  consists,  lie  in  the  infra-red  spectrum  beyond  the  limit  of  this  table.  Fig.  21  is  a  provisional 
spectral  energy-curve  of  the  radiation  of  moist  air  for  the  temperature  +  50°C.  The  positions  of  the 
bands  rest  upon  the  observations  of  Paschen,  Eubens,  and  Aschkinass,  and  relate  to  the  emission 


A 


\ 


01     2    3     4    5    6    7     8    9    10   \\    (2   13    14   \5  \k  (7  18   (9   20  2f   22  23  U 

ffig.  2  i 

Approximate  spectral  energy-curve  of  air  radiation. 

from  aqueous  vapor  and  carbon  dioxide,  with  the  exception  of  the  radiant  energy  of  extreme 
wave-length,  which  I  have  provisionally  assigned  to  one  or  more  of  the  permanent  gases,  nitrogen, 
oxygen,  etc.,  on  the  strength  of  Hutchins'  observation  of  the  absorption  of  air  radiation  by  quartz.* 


LSeep.  112. 


123 

The  form  of  the  curve  will  vary  according  to  the  temperature  arid  composition  of  the  air.  The 
relative  heights  of  the  maxima  are  assumed  to  vary  inversely  as  the  absorption,  but  some  devia- 
tion from  this  rule  must  be  anticipated.  Similar  curves  for  depths  of  air  giving  maximum  radiant 
efficiency  at  the  principal  bands  may  be  constructed  for  other  temperatures  by  first  drawing  the 
appropriate  energy-curve  for  a  black  body,  and  then  inserting  and  graduating  the  heights  of  the 
radiation-bauds,  so  that  the  highest  may  be  included  by  the  curve. 

It  has  been  explained  that  a  considerable  part  of  the  radiation  of  short  wave  length  diffused 
by  the  dust  and  finer  particles  of  the  atmosphere,  reaches  the  surface  of  the  earth.*  Not  so, 
however,  that  portion  of  solar  radiant  energy  which  has  suffered  the  special  absorption  which 
causes  the  cold  bands  of  the  infra  red  spectrum.  This  energy  remains  in  the  air  as  an  increase 
of  temperature,  and  is  subsequently  lost  again  as  atmospheric  radiation ;  but  since  the  greater 
density  and  humidity  of  the  surface  air  obstructs  downward  radiation,  and  since,  further,  in  any 
radiant  interchange  which  can  proceed  through  the  deeper  and  denser  layers  the  excess  of  expendi- 
ture is  in  the  hotter  air,  which  is  usually  beneath,  it  follows  that  atmospheric  radiation,  with  rare 
exceptions,  proceeds  mainly  outward. 

Suppose  that  one- fifth  of  the  entering  radiation  remains  behind  in  a  layer  of  air  20  kilometers 
deep.  Then  during  one  hour  in  the  middle  of  the  day,  the  solar  constant  being  0.03  radim, 
£  X  0.05  x  3600  =  36  small  calories  will  be  imparted  by  the  sun  to  each  column  of  1  sq.  cm.  section 
and  2,000,000  cm.  high.  The  upper  layers  have  the  opportunity  of  attacking  an  unsifted  sunbeam 
and  of  taking  out  those  rays  at  the  baud-centers  which  are  totally  absorbed  by  very  small  quanti- 
ties of  matter.  Hence  in  spite  of  the  rarefaction  of  the  air  and  of  its  chief  absorbent  at  high 
altitudes,  the  absorption  per  unit  of  absorbent  material  being  very  much  greater  at  the  start,  the 
actual  distribution  of  absorption  at  different  altitudes  may  be  tolerably  uniform.  If  the  heat 
developed  in  the  extinction  of  solar  rays  is  distributed  uniformly  through  the  entire  20  kilometers, 
each  kilometer  receives  1.8  small  calories  in  a  vertical  column  of  1  sq.  cm.  section  during  one  hour 
in  the  middle  of  the  day,  and  the  consequent  elevation  of  temperature  is  0.7°  C.  at.  an  altitude  of 
20,000  meters,  but  only  0.07°  C.  at  a.  height  of  1,000  meters.  The  upper  part  of  the  first  layer, 
because  it  receives  the  undepleted  rays,  will  continue  to  absorb  with  the  same  intensity  during 
the  hours  of  sunshine,  and  the  entire  layer  on  account  of  the  obliquity  of  the  rays  and  longer  paths 
with  a  low  sun  will  absorb  more  powerfully  as  the  sun's  altitude  diminishes,  and  at  the  equinoxes 
might  have  its  temperature  raised  at  least  8.4°  in  one-half  day  if  none  of  the  heat  were  lost;  but 
as  the  losses  certainly  exceed  the  gains,  the  diurnal  range  is  not  likely  to  be  more  than  one-half 
of  this  amount. 

The  deeper  layers  of  air  receive  solar  radiation  which  has  been  depleted  of  its  more  absorb- 
able  rays,  and  as  the  sun  nears  the  horizon  a  relatively  larger  part  of  the  energy  remains  in  the 
upper  air,  whence  the  lowest  layers  may  not  be  heated  in  one-half  day  more  than  four  or  five 
times  as  much  as  in  one  hour  at  midday,  and  the  diurnal  range  of  temperature  due  to  absorption 
of  solar  rays  probably  does  not  exceed  two  or  three  tenths  of  a  degree  in  the  2  or  3  kilometers  of  air 
above  the  surface.  Very  much  larger  ranges  occur  in  the  first  1,000  meters  from  the  ground,  but 
they  are  due  to  ascent  of  air  heated  by  contact  with  the  soil  and  cease  at  an  altitude  of  about 
1,000  meters,  where  the  lower  cumulus  clouds  mark  the  upper  limit  of  this  convection.  (See 
"Exploration  of  the  arr  by  means  of  kites"  at  the  Blue  Hill  Meteorological  Observatory,  Ann. 
Harvard  Coll.  Astron.  Obs.,  vol.  42,  part  1,  p.  103,  1897.)  Only  in  case  the  previous  sifting  had 
deprived  the  sunbeam  of  all  of  its  absorbable  rays,  or  provided  the  thermal  energy  were  lost  by 
reradiation  as  fast  as  it  is  received,  could  there  be  a  complete  absence  of  thermal  effect. 

The  advancing  part  of  an  anticyclone  receives  air  directly  depleted  of  moisture  in  the  pre- 
ceding area  of  precipitation.  The  dry  air  is  a  bad  radiator,  and  the  full  increment  of  temperature 
by  compression  in  the  descending  air  is  preserved.  Hence  the  adiabatic  rate  of  cooling  in  unsat- 
urated  air  with  increase  of  altitude  is  maintained  or  exceeded  in  the  front  part  of  the  anticyclone, 
as  Clayton  has  observed  (loc.  cit.,  p.  118).  But  in  the  western  part  of  the  anticyclone  and  the 
advancing  region  of  a  following  cyclone  the  greater  easterly  velocity  of  the  upper  air  carries  along 


'See  the  previous  chapter  on  atmospheric  dust,  p.  118. 


124 


an  overhanging  mass  of  warm,  moist  air  which  diminishes  or  reverses  the  upward  fall  of  tempera- 
ture. The  alternation  of  hot  and  cold  waves  in  winter  brings  a  considerable  range  of  temperature 
in  the  lower  air  which  must  not  be  confounded  with  that  produced  by  the  direct  absorption  of 
solar  radiation. 

The  depth  of  20  kilometers  has  been  taken  as  denning  somewhat  approximately  the  part  of 
the  atmosphere  within  which  water-vapor  can  exist  in  appreciable  quantities  or  what  may  be 
called  the  aqueous  atmosphere. 

It  is  evident,  after  what  has  been  said  in  regard  to  the  small  depth  from  which  atmospheric 
radiation  can  pass  freely,  that  radiant  emission  from  so  great  a  depth  of  air  as  20  kilometers,  or 
even  from  a  small  fraction  of  a  kilometer,  can  only  take  place  by  the  slow  process  of  one  portion 
of  air  radiating  to  a  neighboring  one  which  is  at  a  slightly  lower  temperature,  and  this  in  turn  to 
other  volumes  not  far  away,  the  process  being  repeated  over  and  over  again  until  the  upper 
regions  of  freer  transmission  are  reached. 

The  curve  of  transmission  of  radiation  by  the  terrestrial  atmosphere,  given  in  fig.  22,  is 
intended  to  represent  only  the  most  important  features.  It  relates  to  a  vertical  transmission 
through  a  clear  air  of  only  moderate  humidity,  and  includes  (1)  the  general  fact  of  selective 
sniftering  of  short  waves,  (2)  the  progressive  strengthening  of  baud  absorption  in  the  infra-red, 

100  % 


so 

70 
60 
SO 
40 
30 


<0 
0 


01 


WJ     A 

0  0 


2     3     4     5     6_    7     8 

ca    co. 


10    1M2    13   U   15   f6    17  i8    i9   20  ^\  JUL 


of  radiation  by  the  Earth"1  s  atmosphere, 

due  mainly  to  water-vapor,  including  bands  at  O.Ooj/,  1.1;*,  1.4//,  1.9jw,  2.5ju,  and  4.7/Y,  until  (3)  the 
great  bands  of  this  substance  between  5yu  and  8/<,  marked  £  in  the  figure  (strongest  absorption 
at  5.9/^,  6.5//,  and  7.5^),  are  reached,  (4)  the  greater  but  decreasing  transmission  beyond  9/*  with 
absorption-bands  at  0.0/y,  lO.O^u,  11.6/y,  12.4^,  13.4//,  14.3;/,  15.7^u,  17.5//,  and  perhaps  at  20/v,  still 
attributable  to  aqueous  vapor,  with  the  exception  (5)  of  a  wide  band  extending  from  12.5yu  to  16yu 
with  a  maximum  of  absorption  at  14.7^,  denoted  by  A  in  the  figure,  which  with  the  band  at  4.3/< 
and  the  smaller  one  at  2.7^,  is  produced  by  carbon  dioxide,  and  finally  (0)  a  region  of  almost  total 
absorption  beyond  20w,  here  provisionally  attributed  to  the  permanent  gases  of  the  atmosphere. 


125 

The  absorption  by  carbon  dioxide,  by  water-vapor,  and  possibly  also  by  the  permanent  gases, 
practically  obliterates  the  solar  spectrum  beyond  13;/,  since  the  unabsorbed  radiation  is  here  very 
feeble. 

Some  of  th  '  consequences  of  atmospheric  absorption  may  be  briefly  pointed  out.  The 
absorbent  action  of  carbon  dioxide  and  the  permanent  gases  is  almost  invariable;  but  the  absorp- 
tion bands  of  aqueous  vapor  are  much  stronger  in  summer  than  in  winter,  and  the  selective 
scattering  of  short  waves  also  increases  in  summer.  One  result  of  this  variation  is  that  the  direct 
rays  of  the  midday  sun,  received  upon  a  normal  surface,  are  more  powerful  in  winter  than  in 
summer,  in  spite  of  the  greater  distance  traversed  by  the  sunbeam  through  the  air  in  winter. 
Dr.  Emil  Bessels*  noted  that  the  rays  of  the  arctic  sun  in  early  spring,  although  making  a  very 
small  angle  with  the  horizon  and  penetrating  a  great  depth  of  air,  affected  the  actiuouieter  much 
more  intensely  than  later  in  the  season  after  the  sun  had  risen  higher,  but  when  the  air  had  become 
rnoist.t 

The  direct  effect  of  the  sun's  rays  upon  a  normal  surface  is  less  in  the  tropics  than  in  temperate 
regions,  and  less  at  sea  level  than  upon  a  mountain  top,  owing  to  the  difference  in  the  aqueous 
component  of  the  air;  and  the  ability  of  the  solar  radiation  to  maintain  a  high  temperature  in  the 
torrid  zone  or  at  sea  level  is  due  to  the  accumulation  of  the  thermal  energy  imparted  to  the  Earth's 
surface  by  reason  of  the  retention  of  the  escaping  radiation  from  that  surface  by  a  moist  and 
highly  absorbent  atmosphere  rather  than  to  the  direct  power  of  the  sunbeam.  The  position  of  the 
great  water  band  (E  in  fig.  L"2)  covers  a  region  of  the  infra  red  spectrum  in  which  terrestrial 
radiation  is  near  its  maximum,  and  the  emission  from  the  soil  is  still  strong  at  the  great  A  band; 
but  the  sun's  rays  are  most  powerful  in  the  visible  spectrum  where  aqueous  absorption  is  small 
and  the  bands  of  carbon  dioxide  completely  lacking.  Thus  the  penetrative  power  of  the  incoming 
is  greater  than  that  of  the  outgoing  rays,  and  this  relative  difference,  which  increases  with  the 
amount  of  moisture  in  the  air,  produces  an  accumulation  of  thermal  energy  at  the  Earth's  surface, 
which  would  generate  a  very  high  temperature  were  it  not  that  the  sign  of  the  function  is  reversed 
after  sundown.  The  cumulative  effect  of  continuous  sunshine  gives  a  mild  summer  to  the  arctic 
regions  with  a  sun  of  lower  altitude  than  that  which  brings  vigorous  winter  weather  in  lower 

s  Scientific  Results  of  the  r.  £.  Arctic  Expedition.  Steamer  Polaris.  Vol.  I,  Washington,  1876.  $  Solar 
Radiation,  pp.  80-82. 

tin  Lieutenant  Ray's  Report  of  the  International  Polar  Expedition  to  Point  Barroiv,  Alaska  (Washington,  1885), 
differences  of  black  and  bright  bulb  thermometers  are  given  for  this  station  between  February  1  and  August  27, 
1883.  During  the  mouth  of  March  differences  above  45°  F.  were  measured  on  twelve  days,  during  April  on  fourteen 
days,  during  the  first  half  of  May  on  seven  days ;  but  after  this  the  differences  did  not  again  reach  45°.  In  June  a 
difference  greater  than  40°  was  only  attained  on  three  days,  and  during  July  and  August  the  excess  of  the  black  bulb 
did  not  once  reach  40;.  This  sequence  of  low  readings  is  no  doubt  partly  due  to  the  greater  cloudiness  of  the 
summer  months,  for  the  black-bulb  thermometer  requires  time  to  reach  a  maximum  reading  which  often  fails  to  be 
recorded  during  the  brief  intervals  between  clouds.  Nevertheless,  the  highest  reading  of  all,  82°. 3  F.,  being  made 
on  the  8th  of  May,  which  has  its  parallel  in  the  frequent  maximum  reading  at  9  or  10  a.  m.  in  a  diurnal  curve  of 
intensity,  confirms  the  result  of  Dr.  Bessels,  and  with  many  other  similar  facts,  proves  that  altitude  of  the  sun 
above  the  horizon  is  not  the  only  important  factor  conducing  to  intense  solar  radiation. 

The  reader  may  al.so  consult  the  Report  on  the  Proceedings  of  the  V.  S.  Expedition  to  Lady  Franklin  Bay,  by 
Adolphus  W.  Greely,  vol.  2,  p.  377.  Chart  No.  17  (Washington,  1888).  The  curve  of  solar  radiation  attains  its 
maximum  in  May,  and  ir  is  noted  that  "the  effect  of  increasing  humidity  or  aqueous  vapor  in  intercepting  the  solar 
[radiant]  heat  is  shown  in  a  most  marked  manner.'' 

These  observations  of  solar  radiation  were  made  with  conjugate  bright  and  black  bulb  thermometers  in 
vacuum  chambers  of  glass,  an  instrument  which,  as  we  now  have  it,  is  not  capable  of  giving  accurate  quantitative 
values.  The  chamber  is  supposed  to  be  a  vacuum,  but  there  is  usually  no  means  of  verifying  the  supposition. 
Minute  quantities  of  certain  vapors;  coudensible  at  low  temperatures  but  evaporated  in  hot  sunshine,  may  alter 
the  indications  widely.  If  it  is  desired  to  get  rid  of  all  convection  and  penetration  of  gaseous  molecules  within  the 
envelope,  a  'very  perfect  vacuum  must  be  obtained,  and  variations  either  in  the  degree  of  exhaustion  or  in  the 
material  of  the  transmitting  walls  will  produce  serious  discrepancies  in  instruments  exposed  side  by  side.  Glass 
also  does  not  transmit  the  longer  radiations  readily,  and  the  amount  rejected  will  vary  with  the  thickness  and 
quality  of  the  glass,  with  the  nature  of  the  surrounding  surfaces,  and  especially  with  the  previous  depletion  in 
passing  through  the  atmosphere,  which  is  the  very  thing  we  are  seeking.  A  part  of  the  heat  registered  comes  from 
short- waved  sky  reflection,  and  this  is  relatively  greater  with  a  low  sun;  nevertheless  the  existence  of  an  absolute 
low-sun  maximum  radiation  can  not  be  thus  explained,  and  since  the  chief  defect  of  the  instrument  is  that  it  shuts 
out  much  of  the  radiation  of  long  wave-length  and  obscures  its  variation,  it  is  quite  possible  that  a  perfect  acti- 
nometer  would  show  as  great  or  greater  seasonal  fluctuations. 


126 

latitudes,  continuity  of  accumulation  more  than  compensating  the  advantage  of  greater  trans  mis 
sion  in  winter. 

The  beat  entrapped  through,  the  differential  transmission  of  solar  and  terrestial  radiation  by 
aqueous  vapor,  and  carbon  dioxide  is  mainly  stored  in  the  lower  layers  of  the  atmosphere,  and 
because  the  absorption  by  air  heavily  loaded  with  moisture  is  nearly  complete  for  its  own  radia- 
tion, this  stored-up  energy  continues  for  a  long  time  as  a  controlling  balance  wheel  in  the  mechan- 
ism of  the  weather.  As  long  as  the  mantle  of  water  vapor  remains  unbroken,  thermal  fluctuations 
are  kept  within  narrow  limits.  Storms  may  make  inroads  upon  the  continuity  of  this  aqueous 
atmospheric  envelope,  but  evaporation  of  moisture  restores  the  rents.  Rolled  up  in  great  bosses 
covering  hundreds  of  thousands  of  square  miles  of  territory,  the  thickened  mantle  of  vapor  brings 
hot  waves.  Displaced  by  downward  movements  bringing  the  dry  air  of  the  upper  atmosphere  to 
the  surface,  corresponding  cold  waves  result.  The  gradual  accumulation  of  moisture  in  higher 
and  higher  atmospheric  layers  during  the  summer,  clothes  the  temperate  regions  with  so  deep  a 
protective  covering  of  moist  air,  that  summer  conditions  are  prolonged  in  the  autumn  to  a  time 
which  is  astronomically  the  correlative  of  late  winter.  The  absence  of  this  deep  protective  layer, 
whose  formation  can  only  be  effected  gradually,  permits  late  frosts  in  spring,  long  after  the  sun 
has  resumed  his  ascendency.  In  the  middle  of  a  sunshiny  day,  by  the  evaporation  of  moisture 
from  the  earth's  surface  and  its  ascent  in  convection  currents,  the  vapor  of  water  is  carried  up  to 
high  levels;  but  during  the  night  most  of  this  accession  of  moisture  is  diffused  into  colder  or  drier 
regions  of  the  upper  air,  where  it  is  either  condensed  and  no  longer  exists  in  the  air  as  vapor,  or 
is  so  diluted  and  reduced  in  relative  humidity  as  to  be  of  slight  absorptive  value  when  the  sun 
next  rises.  The  increase  of  moisture  in  the  upper  air  at  midday  is  the  cause  of  the  flat-topped 
diurnal  actinornetric  curves  which  are  observed  on  all  but  the  coldest  and  driest  days.  As  the  sun 
mounts  above  the  horizon,  the  intensity  of  his  rays  augments,  giving  an  actiuometric  curve,  which, 
on  an  exceptionally  dry  day,  is  approximately  a  parabola,  symmetrical  about  the  midday  ordinate; 
but,  in  general,  the  apex  of  the  curve  is  truncated,  and  after  about  9  a.  in.  the  curve  becomes  flat- 
topped  with  minor  fluctuations  indicating  the  activity  of  the  convective  process,  and  the  passage 
of  invisible  clouds  of  vapor  across  the  line  of  sight.  At  the  same  time  the  curve  of  relative 
humidity  of  the  surface  air  becomes  deeply  depressed,  while  at  high  levels  the  tension  of  aqueous 
vapor  increases  in  the  middle  of  the  day,  indicating  the  rapid  removal  of  aqueous  vapor  from  the 
lower  to  the  upper  air.  The  earth  has  its  lowest  temperature  and  the  air,  if  clear,  its  greatest 
transmission  in  the  early  morning  hours  when,  as  a  whole,  the  atmosphere,  according  to  observa- 
tions at  high  levels,  has  its  smallest  content  of  aqueous  vapor,  a  condition  which  is  evidently  cor- 
related with  the  maximum  actinometric  effect  observed  by  Bessels  in  the  arctic  spring  months. 

It  appears  certain  that  on  our  Earth  surface  temperatures  lower  than  —  73°  C.,  or  200°  absolute, 
can  not  occur,  possibly  because  of  the  almost  total  absorption  by  the  atmosphere  of  all  radiations 
beyond  13//.  Paschen's  law  of  the  wave-length  of  the  maximum  in  the  normal  spectral  energy- 
curve  of  a  black  body  gives  at  this  temperature  : 


Thus  the  position  of  the  no.rmal  maximum  in  the  energy-curve  for  the  lowest  arctic  temperature 
very  nearly  coincides  with  the  great  absorption  -band  of  carbon  dioxide  (  J,  fig.  22),  discovered  by 
Eubens  and  Aschkiuass;  and  at  lower  temperatures  the  maximum  would  be  found  at  still  greater 
wave-lengths  on  which  the  permanent  gases  of  the  atmosphere  may  possibly  exercise  a  complete 
absorption.  In  the  midst  of  much  conflicting  testimony  as  to  the  region  of  the  spectrum  in  which 
the  absorption  of  pure  air  resides,  this  suggestion  is  at  least  worthy  of  consideration. 

By  the  same  law  a  sunlit  surface  of  rock  at  340°  absolute  temperature,  if  radiating  like  a 
black  body,  must  have  its  spectral  maximum  at  8.5/<;  and  taking  the  mean  temperature  of  the 
earth  as  -4-  15°  C.,  its  spectral  maximum  would  reside  on  the  average  at  10//.  Some  deviation 
from  the  law  is  to  be  expected  and  does  occur  in  the  spectra  of  solids,  which  do  not  conform  to 
the  ideal  of  blackness.  Since  it  appears  to  be  a  general  law  that  the  radiation  of  a  body  is 
especially  large  in  that  spectral  region  where  its  absorption  is  exercised,  it  is  possible  that  the 
radiation  of  the  ocean  at  a  mean  surface  temperature  of  -f-  15°  C.  will  be  found  to  have  the  maxi- 


127 

mum  in  its  spectral  energy-curve  displaced  to  a  wave-length  shorter  than  10//,  and  approaching 
the  great  band  (Z)  where  the  absorption  of  atmospheric  moisture  is  greatest,  and  that  this  is 
another  cause,  in  addition  to  the  large  specific  heat  and  mobility  of  water,  conducing  to  the 
slowness  of  oceanic  temperature  changes;  but  more  important  as  a  retainer  of  oceanic  heat  is  the 
extension  of  the  band  -.  to  greater  wave-lengths  in  the  absorption  of  the  layer  of  air  nearly 
saturated  with  moisture,  which  always  hangs  over  the  water. 

The  absorption  of  terrestrial  radiation  by  atmospheric  moisture  lies  somewhere  between  such 
curves  as  those  of  figs.  14  and  15.  Aqueous  absorption  is  very  greatly  increased  as  the  air 
approaches  saturation,  because  the  molecules  of  water-vapor  then  become  complex  and  have  an 
absorptive  power  approaching  that  of  liquid  water.*  The  absorption  of  the  atmosphere  and  the 
surface  temperature  which  can  be  maintained  by  its  aid,  increase  both  with  the  absolute  and  with 
the  relative  humidity. 

Not  only  is  the  absolute  temperature  of  the  soil  dependent  upon  atmospheric  moisture,  acting 
in  conjunction  with  the  heat  supplied  by  the  sun's  rays,  but  also  the  diurnal  range  of  surface 
temperature.  "  Where  the  laud  is  moist  the  changes  of  temperature  are  less  than  where  it  is  dry 
or  arid,"  but  it  is  the  condition  of  the  air  and  not  that  of  the  soil  which  makes  the  radiation 
possible  or  impossible.  The  following  illustration  under  nearly  the  same  insolation  must  suffice 
as  an  example. 

After  several  weeks  of  rain  in  May,  the  daily  range  for  the  first  week  of  pleasant  weather  in 
June  was  9°.  5  C.  At  the  beginning  of  August,  after  two  months  of  drought,  the  range  had 
increased  to  12°.  1  0.,  and  the  highest  range  of  the  week  in  June  (10°.  4  C.)  was  less  than  the 
lowest  (10°.  6  C.)  of  the  week  in  the  time  of  greatest  drought. 

TABLE  76. 


* 
Date. 

Kange. 

Sky. 

Date. 

Range.                                        Sky. 

°C. 

o  C. 

June      3 

8.8 

Clear  —  Cirrus. 

July    31 

11.0         Clear,  smoky  —  Cirrus  p.  m. 

4 

10.4 

Alto-cumulus  —  showers. 

Aug.      1 

11.9             "            "         cloudv  evening. 

5 

9.2 

Cloudy  —  Rain. 

2 

11.  2         Cloudv,  0.01  inch  of  rain. 

6 

8.8 

Cloudy  a.  m.  ;  clear  p.  m. 

3 

12.  8         Cumuli. 

7 

10.4 

Cirrus  —  Cumuli  p.  m. 

4 

14.  5         Clear,  then  cumuli. 

8 

9.5 

Clear  —  Hazy. 

5 

10.  6         Clear. 

9 

9.1 

(t           n 

/> 

12.  4         Clear—  Smoky. 

Mean. 

9.5 

Mean. 

12.1 

On  Pike's  Peak  the  range  is  greater  in  winter  than  on  the  plains,  but  less  in  summer.  Here 
also  the  mountain  climate  is  relatively  drier  than  that  of  the  plains  in  winter  than  in  summer. 

In  free  air  the  diurnal  range  is  small,  but  in  this  case  because  the  radiation  which  has  escaped 
the  previous  action  of  the  chief  absorbent  of  radiation,  water- vapor,  is  deficient  in  absorbable 
rays,  and  small  toll  is  taken  by  the  air.  On  a  mountain,  and  still  more  on  a  plateau,  the  increased 
power  of  the  sun's  rays  heats  the  rocks,  and  thence  the  surface  air,  more  than  at  lower  altitudes, 
and  unless  the  wind  is  so  strong  as  to  remove  the  surface  air  before  ifr  is  much  heated,  replenish- 
ing it  with  cool  air  from  the  free  atmosphere  around  the  mountain  top,  the  range  may  be  greater 
on  the  mountain  than  on  a  low-lying  plain,  because  of  the  more  powerful  insolation. 

The  spectrum  of  the  radiation  of  the  atmosphere  consists  entirely  of  lines  and  bands;  and 
since  the  atmospheric  absorption  acts  within  the  same  limited  regions  of  the  spectrum,  atmospheric 
radiation  is  largely  annulled  by  an  absorption  which  is  identical  in  quality,  or  as  to  the  kinds  of 
rays  affected,  with  the  thing  on  which  it  is  exerted,  and  can  differ  only  in  regard  to  the  rapidity 
with  which  extinction  or  emission  vary  with  the  depth,  or  by  a  redistribution  of  energy,  according 
to  which  the  radiation  in  process  of  transmission  may  be  absorbed  by  one  constituent  of  the 
atmosphere  but  emitted  again  by  a  different  one,  or  passed  on  by  a  series  of  alternate  radiations 
and  absorptions.  In  any  case  the  depth  from  which  atmospheric  radiation  can  directly  proceed  is 


See  p.  100,  et  seq. 


128 

limited,  and  the  amount  of  the  emission  is  relatively  greater  for  a  small  depth.  Hence  laboratory 
experiments  which  deal  with  small  layers  of  air,  give  radiant  values  which  are  too  large  to  be 
applied  without  discrimination  in  meteorological  problems. 

Owing  to  the  feebleness  of  the  radiation-bands  in  the  spectrum  from  air  at  such  moderate 
temperatures  as  prevail  in  the  atmosphere,  and  owing  further  to  the  limitation  of  the  emission  to 
the  outer  layers  of  large  masses  of  air,  small  effect  is  to  be  anticipated  from  the  radiation  of 
elevated  bodies  of  warm  air  to  a  cooler  underlying  surface.  Clayton's  kite  experiments  on  Blue 
Hill  have  demonstrated  the  existence  of  high  warm  layers  of  clear  air  above  cold  layers  and  a  cold 
surface,  when  the  surface  winds  are  from  a  cold  quarter,  and  wheu  the  surface  temperature  has 
been  changed  very  little  by  the  substitution  of  warm  for  cold  air  at  the  upper  level.  Radiation 
effects  are  immediate,  and  it  is  possible  that  under  these  circumstances  a  slight  elevation  of 
temperature  from  the  radiation  of  the  warm  air  may  be  discriminated  in  advance  of  the  slower 
rise  of  temperature  produced  by  the  commingling  of  air  currents  and  the  bodily  transfer  of  super- 
ficial air  from  warmer  regions  by  cyclonic  movement.  The  most  advantageous  occasion  for  testing 
such  a  possibility  is  immediately  after  a  severe  cold  wave  in  winter,  for  then  the  absorbent  power 
of  the  lower  air  for  the  hypothetical  radiation  from  the  warm  upper  layer  will  be  least.  The  return 
of  an  elevated  body  of  relatively  warm  air  after  a  severe  cold  wave  is  usually  heralded  by  an 
increase  of  cirro-stratus  cloud,  and  this  alone  may  make  surface  temperature  greater  by  the  action 
of  the  aqueous  vapor  whose  presence  is  made  known  by  the  cloud,  the  vapor  imprisoning  more  of 
the  sun's  rays  in  the  daytime,  and  impeding  the  escape  of  terrestrial  radiation  at  night. 

I  will  give  two  examples  of  recovery  from  cold  waves,  observed  at  Providence,  R.  I.,  taking 
the  data  from  the  records  of  the  City  Engineer's  Office  and  of  the  Ladd  Observatory. 

Cold  wave  of  January  6  to  10,  1896. — The  minimum  of  —  8°  F.  on  the  morning  of  the  6th  was 
followed  by  a  gradual  recovery,  lasting  four  days.  Bach  day  saw  a  recovery  of  about  7°.  The 
air  on  the  Gth  was  very  dry  (relative  humidity  22  per  cent.).  The  barometer,  which  had  risen  to 
30.37  inches  on  the  evening  of  the  Gth,  fell  very  slowly  to  29.81  inches  on  the  morning  of  the  10th. 
In  this  case  there  was  no  pronounced  cyclone,  but  3  inches  of  snow  fell  from  2  p.  m.  on  the  7th  to 
2  a.  m.  on  the  8th,  and  11  inches  from  3  p.  m.  on  the  9th  to  7  p.  m  on  the  10th.  The  clouds  began 
to  gather  on  the  morning  of  the  7th.  The  wind  continued  north  during  the  four  days,  except  for 
a  short  time  on  the  9th. 

Cold  icave  of  February  16  to  19, 1896. — There  was  a  fall  of  2.5  inches  of  snow,  ceasing  at  3  p.m. 
on  the  16th.  The  thermometer,  which  at  0  a.  m.  on  the  16th  was  42°  F.,  fell  steadily  to  —8°  F. 
on  the  morning  of  the  17th.  The  highest  temperature  on  the  17th  was  -f  7°  F.  at  5  p.  m.  after  a 
day  of  unclouded  sunshine.  The  barometer,  after  7  a.  m  on  the  17th,  was  steady  at  30.30  inches. 
Relative  humidity  rose  slowly  during  the  night  of  the  17th  to  18th  from  40  per  cent,  to  55  per  cent. ; 
lowest  temperature,  0°  F.  at  midnight.  Sky  clear  until  the  morning  of  the  18th,  when  there  was 
a  trace  of  snow  (clouds  0.9);  temperature  +  2°.5  at  6  a.m.,  February  18th,  and  barometer  falling 
(30.20  inches).  Relative  humidity  and  temperature  then  increased  rapidly,  until  at  1 1  p.  m.  snow 
began  to  fall,  continuing  until  9  p.  in.  on  the  19th,  when  the  barometer  had  descended  to  29.27 
inches.  The  wind  continued  north  until  noon  of  the  19th,  when  it  changed  to  the  southeast. 
Here  a  part  of  the  rise  of  10°.5  in  tht;  first  twenty-four  hours  after  the  minimum  must  be  attributed 
to  the  influence  of  sunshine.  More  rapid  recoveries  than  this  are  almost  invariably  accompanied 
by  a  change  of  wind  to  the  south,  or  by  a  sudden  accession  of  moisture,  implying  the  importation 
of  warm  air  from  a  milder  neighborhood. 

The  solar  radiation  of  0.05  radim  often  produces  a  rise  of  temperature  of  15°  C.  between  sun- 
rise and  midday  (no  account  being  taken  of  atmospheric  absorption).  A  rise  of  temperature  at 
the  rate  of  1°.5  C.  in  six  hours  after  a  cold  waye  may  frequently  be  observed,  indicating  a  radiation 
of  0.005  radim,  if  due  to  a  warm  upper  layer  of  air,  assuming  that  the  lower  layers  are  dry  enough 
to  permit  the  passage  of  this  radiation  with  no  more  obstruction  than  that  which  affects  the  sun's 
rays.  An  upper  layer  of  warm  and  moist  air,  10°  C.  above  surface  temperature  and  1  meter 
thick,  will  radiate  0.0002  radim,  but  the  radiation  must  be  twenty-five  times  as  great  if  the 
recovery  of  heat  after  a  cold  wave  is  to  be  attributed  to  direct  atmospheric  emission.  Some  effect 
could  no  doubt  be  produced  by  an  indirect  process  involving  layers  of  considerable  depth,  but 
there  is  no  warrant  for  the  supposition  that  the  warm  upper  currents  in  the  cases  cited  have  an 


129 

excess  of  10°  above  surface  temperature.  The  existence  of  warmer  air  a  few  meters  above  the  soil 
which  is  unduly  chilled  by  nocturnal  radiation  at  the  calm  center  of  an  anticyclone  is  not  in  ques- 
tion here,  for  this  air,  although  it  is  so  near,  being  dry,  does  not  radiate  enough  to  prevent  the 
surface  refrigeration. 

It  seems  probable  that  after  the  descent  of  dry  air  at  the  center  of  an  anticyclone  has  ceased 
and  unimpeded  surface  radiation  to  space  has  produced  the  minimum  surface  temperature  of  a 
cold  wave,  the  gradual  recovery  of  heat  and  moisture  by  the  lower  atmosphere  is  effected  princi- 
pally by  the  absorption  of  the  sun's  rays,  by  evaporation  from  the  surface,  and  by  the  mingling 
of  air  from  warmer  regions,  and  that  any  contribution  which  atmospheric  radiation  from  upper 
warm  layers  may  give  to  this  recovery  of  heat  is  not  likely  to  produce  a  rise  of  temperature  of 
more  than  1°  C.  per  day. 

The  power  of  warm  air  to  radiate  must  depend  largely  on  its  isolation.  An  upper  body  of 
warm  moist  air,  if  fi  eely  suspended  in  the  midst  of  dry  air,  immediately  becomes  a  good  radiator, 
not  only  by  virtue  of  its  high  temperature,  but  because  of  its  containing  an  especially  emissive 
substance.  The  radiation,  however,  owing  to  the  peculiar  absorption  of  its  own  rays  by  the  moist 
air,  can  only  proceed  through  a  small  surface  layer,  which  soon  becomes  saturated  by  the  cooling. 
The  great  increase  of  absorption  which  has  been  shown  to  occur  at  the  condensation  point  of 
water  prevents  further  cooling  by  radiation,  except  in  an  excessively  thin  surface  shell  of  cloud, 
and  it  is  doubtful  if  any  large  proportion  of  rainfall  is  produced  through  cooling  of  moist  air  by 
radiation,  even  in  those  towering  cumulo-nimbi  which  ascend  into  dry  regions  where  the  radiant 
effect  is  greater.  While  cumulus  clouds  may  be  thimble-shaped  shells,  the  typical  rain-cloud 
generates  its  rain,  not  by  any  skin-squeezing  process,  but  by  expansive  cooling  which  affects  the 
entire  volume  of  air.  , 

Air  radiation  must  usually  proceed  more  easily  upward  than  downward,  because  the  higher 
layers  are  apt  to  be  drier  and  more  transmissive  than  the  lower.  Cooling  by  radiation,  although 
of  small  moment  in  the  lower  air,  must  be  added  to  cooling  by  expansion  as  a  cause  for  the  cold 
of  the  high  atmosphere;  and  the  diminution  of  absorption  of  its  own  radiation  by- air  at  great 
altitudes  on  account  of  lessening  aqueous  vapor,  so  far  compensates  for  decrease  of  radiant  power 
at  very  low  temperatures  that  cooling  by  air  radiation  may  be  effective  to  the  outer  limit  of  the 
atmosphere,  and  may  prevent  the  retention  of  such  molecular  velocities  as  would  permit  the 
escape  of  air  molecules,  except  in  the  very  unusual  case  of  the  ejection  of  intensely  hot  vapor  to 
great  heights  by  volcanic  eruptions.  The  former  prevalence  of  vigorous  vulcanism  on  the  Moon 
has  perhaps  had  more  to  do  with  the  loss  of  the  Moon's  atmosphere  than  the  smallness  of  its 
attraction,  at  least  the  fact  that  one  or  more  of  Jupiter's  satellites  exhibit  phenomena  which  are 
presumably  atmospheric,  warns  us  not  to  place  too  great  faith  in  the  theory  that  a  small  planet 
must  necessarily  have  a  relatively  small  atmosphere.  Another  cause  which  has  peculiarly  favored 
the  loss  of  the  Moon's  atmosphere  by  the  escape  of  individual  molecules  of  high  velocity  has  been 
the  slowness  of  its  axial  rotation,  which  permits  an  accumulation  of  heat  during  the  long  day  until 
surface  temperatures  considerably  above  that  of  boiling  water  are  attained.  (See  the  author's 
"Probable  range  of  temperature  on  the  Moon,"  Astroph.  Journ.,  vol.  8,  Nos.  4  and  5,  Nov.  and 
Dec.,  1898). 

The  results  of  the  present  research  prove  that  within  moderate  depths  of  only  a  few  meters 
the  radiation  of  dry  air,  purified  from  carbon  dioxide,  increases  quite  uniformly  with  the  depth; 
that  the  radiation  of  a  1-meter  layer  of  purified  air  at  50°  C.  and  near  atmospheric  pressure 
(735  mm.),  as  compared  with  one  at  0°  C.,  is  0.00068  radim,  representing  a  transformation  and 
transfer  of  thermal  energy  of  0.00068  small  calories  every  second  through  each  square  centimeter 
of  limiting  surface;  that  the  radiation  of  a  like  depth  of  carbon  dioxide  at  the  same  temperature 
is  three  and  one-half  times  that  of  air,  or  0.00238  radiin,  which  is  very  nearly  a  maximum  for  this 
temperature,  further  increase  of  the  radiant  depth  being  unattended  by  a  corresponding  addition 
of  radiant  energy,  showing  that  equilibrium  between  radiation  and  emission  has  been  almost 
reached  at  this  depth;  that  the  radiation  from  a  layer  of  steam  5  feet  deep  at  one-sixth  of  atmos- 
pheric pressure  is  two  and  one-half  times  that  from  a  like  body  of  dry  air  at  temperatures  near  the 
boiling  point  of  water,  and  eight-tenths  of  the  radiant  emission  from  the  black  solid  body;  while 
for  smaller  depths  the  radiant  power  of  water-vapor  is  relatively  greater,  a  steam  jet  of  small 
12812— Bull.  G 9 


130 

dimensions  radiating  over  four  times  as  strongly  as  one  of  air,  a  ratio  which  would  doubtless  have 
been  considerably  greater  if  the  air  had  been  perfectly  dry. 

There  appears  to  be  no  reason  to  doubt  that  the  radiation  of  a  moderate  depth  of  homogeneous 
air  at  a  given  temperature  depends  on  the  product  of  the  depth  by  the  density,  and  remains  the 
same  when  depth  and  density  vary  inversely;  but  the  absorption  of  a  given  mass  of  aqueous  vapor 
has  been  found  to  be  smaller  when  distributed  through  a  large  volume  of  air  than  when  concen- 
trated.* The  phenomena  are  conditioned  by  molecular  relations.  Beciprocal  variation  of  depth 
and  density  does  not  change  the  number  of  molecules  which  are  engaged  in  the  radiant  transaction 
in  a  homogeneous  medium;  but  dilution  by  another  substance  involves  a  partition  of  energy 
among  molecules  whose  radiant  and  absorbent  properties  are  dissimilar. 

As  an  absorbent  of  terrestrial  radiation  aqueous  vapor  is  very  much  more  efficient  than  any 
other  atmospheric  ingredient;  but  as  radiators  when  in  large  masses,  the  substances  which 
compose  the  atmosphere  do  not  differ  as  widely  as  might  be  supposed,  and  the  position  of  chief 
radiant  may  be  assumed  in  turn  by  either  aqueous  vapor,  carbon  dioxide,  or  the  permanent  gases, 
according  as  the  depths  and  temperatures  of  the  emissive  and  absorbent  layers  change.!  The 
depth  of  gas  which  gives  maximum  radiation  at  short  range  is  an  insignificant  quantity  compared 
with  atmospheric  dimensions,  and  radiation  from  either  the  atmosphere  of  the  Earth  or  the  solar 
chromosphere  is  a  superficial  phenomenon,  even  when  the  masses  of  heated  gas  measure  thousands 
of  miles  in  thickness.  The  fineness  of  the  chromospheric  lines  in  the  solar  spectrum,  although 
the  shifts  of  the  Fraunhofer  lines  indicate  pressures  of  many  atmospheres  at  the  base  of  the 
chromosphere,  is  a  sufficient  demonstration  that  only  the  outer  layers  radiate.  If  the  emission 
proceeded  also  from  the  depths  of  the  chromospheric  mass,  the  lines  of  hydrogen  and  some  other 
elements  would  be  greatly  widened ;  and  if  the  Earth's  atmosphere  radiated  unimpeded  throughout 
its  depth,  its  thermal  changes  and  its  radiant  effects  would  be  enormous.  Instead  of  this,  we 
find  the  atmosphere  playing  the  part  of  a  conservator  of  thermal  energy,  and  must  gratefully 
admire  the  beneficent  arrangement  which  permits  the  Earth  to  be  clothed  with  verdure  and 
abundant  life. 

*  See  p.  94. 

t  This  statement  can  not  be  absolutely  verified,  because  tlie  dimensions  of  my  apparatus  were  insufficient  to 
give  the  maximum  radiation  for  pure  air,  but  it  is  strongly  indicated  by  the  curves  and  on  theoretical  grounds. 


ANALYTICAL   TABLE   OF   CONTENTS. 


Page. 

Letter  of  transmittal . . . -  - 3 

Prefatory  note , ....- -- - 5 

MEASURING  INSTRUMENTS. — THE  BOLOMETER.. 6 

Computation  of  currents  by  simple  theory  of  Wheatstone's  bridge ,.  7 

Reid's  theory  of  the  bolometer 8 

Relative  efficiency  of  the  same  bolometer  with  different  areas  exposed 10 

Influence  of  a  temperature-gradient  in  the  bolometer  strips 10-11 

Tests  of  efficiency  of  bolometers —  12 

Disturbances  produced  by  convection 13 

Radiation  and  convection  rates  in  thermometers  and  bolometers 14-15 

Rate  of  heating  of  thin  black  platinum  by  radiation 16 

THE  GALVANOMETER  -  - -  16 

Mode  of  astaticizing .. . . .  — 17 

Specific  magnetism  of  hollow  magnets  used  in  galvanometer  needle 18 

Determination  of  resistance  of  battery  by  half-deflection  method 18 

Measurement  of  galvanometer  shunt ..  — .--• 19 

Measurement  of  galvanometer  constant 20 

Logarithmic  decrements  for  galvanometer  needle 20 

Suspension  of  needle  . .  1 -. 21 

Variation  of  magnetic  field ..,,. 21 

SCREENS  (USED  IN  STANDARDIZING  INSTRUMENTS) 21 

Computation  of  reduction  factors  for  instrumental  readings  obtained  with  different  apertures 22-23 

Screen  comparisons  and  valuation  of  standard  deflections. .- 23-25 

Adopted  values  of  instrumental  readings  in  absolute  units  of  radiation 26 

PSYCHROMETER  FACTOR . -  -- 26 

Air  depths  and  equivalent  layers  of  absorbent  water  in  different  pieces  of  apparatus 28 

DESCRIPTION  OF  METHOD  A  AND  APPARATUS .  - 28 

Dimensions  of  movable  air  chambers  and  apertures ... ..  -•- ..        29 

Correction  for  the  magnetic  effect  of  the  apparatus  during  motion  in  Method  A 30 

Observations  of  air  radiation  by  Method  A 31-34 

Apparent  small  transmission  of  air  radiation  by  glass. ...: 34 

Discontinuity  of  the  absorption  by  glass  in  the  infra-red  spectrum . 35 

Computed  radiation  of  lampblack  at  the  given  temperatures. 35 

Observed  radiations  (subsequently  shown  to  be  only  in  part  atmospheric) 36 

Examination  of  Professor  Hutchins'  hypothesis  "  that  radiation  takes  place  only  when  there  is  a  fall  of 

temperature  u-ithin  the  limits  of  molecular  action " 36 

DESCRIPTION  OF  METHOD  B 37 

Method  of  determining  thermal  gradient  and  mean  temperature  of  ascending  air  vein  with  first 

arrangement  of  apparatus    .  38-39 

Measured  air  radiation  with  first  arrangement. 40 

Measurements  of  thermal  gradients  of  air  vein  in  second  arrangement  of  apparatus 41-42 

Observed  values  of  air  radiation  with  second  arrangement  .... 43-44 

Observed  values  (Method  B)  reduced  to  a  depth  of  1  meter  and  temperature  40  °  C 44 

DESCRIPTION  OF  APPARATUS  AND  METHOD  C .  - 44 

Dimensions  and  plan  of  radiation  cylinder 45 

General  theory  of  the  Apparatus  C ... . .         46 

Evidence  of  discontinuity  of  thermal  distribution  in  the  radiating  gaseous  mass  when  heated  from 

below,  requiring  the  rejection  of  certain  measures,  but  proving  the  gaseous  origin  of  the  radiation.        47 

Distribution  of  temperature  (heating  cylinder) 48 

Distribution  of  temperature  (cooling  cylinder) 49 

Abnormal  radiant  values  (heating  cylinder)  . .. . . 50-51 

Change  of  sign  of  apparent  air  radiation  when  temperature  inequalities  are  extreme 52 

Analysis  of  the  last  experiment 53 

131 


132 

Page. 

METHOD  C. — EXPERIMENTS  ix  WHICH  THE  DEPTH  AND  PRESSURE  OF  THE  AIR  ARE  VARIED 54 

First  measures  with  air  and  with  carbon  dioxide .._ . 54 

More  elaborate  observations  on  CO; 55-59 

Determination  of  the  variation  of  apparent  radiation  of  CO>  with  change  of  depth 59 

Comparison  of  rates  of  increase  of  radiation  with  temperature  for  a  3-inm.  layer  of  COj  (deduced 

from  Paschen's  curves),  and  for  a  layer  of  1418  mm.  determined  by  the  present  observations. .. .  59-60 
Comparison  of  the  apparent  radiations  of  air  and  of  CO-  at  different  depths  expressed  as  percent- 
ages, showing  nearly  uniform  change  in  air,  but  rapid  diminution  of  radiant  increments  with 

increase  of  depth  in  CO- 60 

Limitation  of  the  effective  radiant  depth  in  carbon  dioxide. . 61 

Radiation  from  multiple  flames  . . 61 

Evidence  of  self -absorption  of  flame  radiation  by  successive  flames,  and  of  further  absorption  by 

the  aqueous  vapor  of  the  room . . . 62 

Measurements  of  air  radiation  and  of  COi  radiation  made  during  cumulative  heating  of  gaseous  masses .  62 
Measurements  of  gaseous  radiation  made  during  gradual  cooling  of  the  gasemis  masses  and  with  com- 
paratively uniform  temperature  gradients - 66 

Apparent  gaseous  radiation  by  Method  C , -.- 70 

Experiment  on  the  radiation  of  steam 72 

Explanation  of  results  at  loiv  pressure , . 72 

METHOD  D. — RELATIVE  RADIATION  OF  AIR  AND  STEAM  AND  OF  CLEAR  AND  SMOKY  AIR 73 

COMPARISON  OF  SOME  OF  THE  PRECEDING  RESULTS  WITH  THOSE  OF  TYNDALL . __  75 

Radiation  of  gases  dynamical! y  heated  by  compression - 76 

Radiation  from  different  depths  of  CO^ ... - 77 

MODIFICATION  OF  ATMOSPHERIC  RADIATION  BY  THE  ABSORPTION  OF  CONSTITUENT  GASES  AND  VAPORS.  .  78 
ABSORPTION  OF  RADIATION  BY  AQUEOUS  VAPOR  AND  GENERAL  CONSIDERATIONS  CONCERNING  ABSORP- 
TION BY  VAPORS  AND  GASES - . 78 

Quotations  from  Ferrel's  ' '  Recent  Advances  in  Meteorology  " 79 

Magnus'  criticism  of  Tyndall's  work  and  its  refutation 80 

Discrepancies  in  Tyndall's  results,  not  hitherto  noticed. 81 

Hoorweg's  measures  of  aqueous  absorption - 81 

Buff's  modification  of  Magnus'  method -  82 

•  Tyndall's  refutation  of  Buff's  criticism - --  83 

Quotation  from  Davis'  "Elementary  Meteorology".. 83 

Quotation  from  Preston's  "  Theory  of  Heat "      84 

Observations  by  Lecher  and  Pernter,  and  by  Tyndall,  compared 85 

Regnault's  observation  of  a  variation  in  the  density  of  aqueous  vapor 85 

Comparison  of  observations  by  Tyndall  and  by  Lecher  and  Pernter  on  the  transmission  of  radiation 

by  ether- vapor. ... - --  86 

Criticism  of  the  estimate  of  aqueous  absorption  drawn  by  Lecher  and  Pernter  from  Violle's 

measurements  of  solar  radiation  at  top  and  bottom  of  Mount  Blanc 87 

Tyndall's  final  paper  in  1882,  containing: 

(a)  Further  criticism  of  later  observations  by  Magnus  on  the  radiation  of  aqueous  vapor 88 

( 6)  Measurement  of  aqueous  absorption  of  radiation  from  a  hydrogen  flame 88 

(c)  Proof  that  absorption  of  radiation  by  ether- vapor  is  constant  if  the  product  of  depth  by 

pressure  remains  the  same .. . . .   89 

(d)  Observation  of  equality  of  vaporous  and  liquid  absorptions  of  radiation  from  various  sources 

in  the  cases  of  ethyl  ether  and  arnyl  hydride,  and  incorrect  general  conclusion  drawn  by 

Tyndall  from  these  facts -  - -  89 

(e)  Observations  of  variations  of  pressure  in  gases  produced  by  radiation  and  depending  on 

combined  radiative  and  absorptive  powers  of  the  gas 90 

Absorption  of  radiation  from  a  red-hot  spiral  by  liquid  water  (Tyndall) .  90 

Absorption  of  radiation  from  lampblack  near  100    C.  by  the  aqueous  vapor  of  the  atmosphere 

(Langley  and  Very) .... -- 

Preliminary  conclusion,  drawn  from  a  comparison  of  these  observations,  that  aqueous  absorption 

of  radiation  varies  with  the  relative  humidity  of  the  air  and  with  the  physical  state  of  the  water.  92 

Spectral  energy-curve  of  lampblack  near  100°  C.  absorbed  by  water- vapor  in  the  atmosphere  . .  92 

Spectral  energy-curve  of  hot  sheet-iron  absorbed  by  steam  (Paschen) _  93 

Evidence  that  concentrated  water-vapor  absorbs  radiation  more  powerfully  than  an  equal  amount 

of  vapor  largely  diluted  by  air _ -                        -   -  94 

Spectral  energy-curves  of  black  platinum  at  450   C.  absorbed  by  various  depths  of  liquid  water 

(measured  from  Paschen 's  figures )  9~> 

Examples  of  a  new  mode  of  derivation  of  the  transmission  of  total  radiation  from  any  source: 

a.  Temperature  of  source  100°  C  .....  -  95-96 

b.  Temperature  of  source  81  "r  C.  (?) -  97-98 


133 

MODIFICATION  OF  ATMOSPHERIC  RADIATION,  ETC. — Continued.  Page. 

ABSORPTION  OF  RADIATION  BY  AQUEOUS  VAPOR,  ETC. — Continued. 

Curves  of  absorption  of  total  radiation  by  liquid  water 98 

Determination  of  ratio  of  aqueous  liquid  and  vaporous  absorptions  of  total  radiation 99 

Observation  by  Liveing  and  Dewar  of  two  sorts  of  oxygen  absorption-bands  (linear  and  diffuse), 

corresponding  in  all  probability  to  molecules  of  different  complexity 99 

Observation  by  Ramsay  and  Shields  of  various  degrees  of  complexity  in  the  molecules  of  liquid 

water 100 

Suggestion  that  the  remarkable  increase  of  absorption  of  radiation  by  aqueous  vapor  as  saturation 
is  approached,  and  the  corresponding  increase  of  vapor  density  observed  by  Regnault,  may  be 

due  to  the  formation  of  a  limited  number  of  complex  molecules  in  the  vapor _ . . 100 

Paschen's  observations  of  the  spectral  positions  of  absorption-bands  due  to  liquid  water. 100 

Paschen's  identification  (in  1894)  of  aqueous  and  carbon  dioxide  absorption-bands  (between  l/<  and 
8//),  as  observed  by  him,  with  the  telluric  absorption-bands  of  the  solar  spectrum  measured  as  to 

intensity  and  position  by  Langley - 101 

Shifting  of  position  of  maximum  in  bands  of  radiant  emission  from  heated  water-vapor  with  chang- 
ing temperature  (Paschen) ,.. - -  -  102 

First  photographs  of  diffuse  infra-red  absorption-bands  of  liquid  water  by  Abney  and  Festing  in 
1883,  and  discovery  of  two  kinds  of  aqueous  bands  (linear  and  diffuse)  due  to  atmospheric  moist- 
ure, the  diffuse  increasing  with  the  relative  humidity,  and  probably  attributable  to  the  complex 

molecules  discovered  10  years  later  by  Ramsay  and  Shields 103 

First  quantitative  measures  of  spectral  energy-curves  of  the  positive  carbon  of  an  arc-light  after 

absorption  by  liquid  water,  made  with  a  linear  thermopile  by  Abney  and  Festing  in  1883,  and 

here  stated  as  percentage  transmissions  at  points  of  spectral  maximum  and  minimum  energy, 

proving  that  nearly  all  of  the  infra-red  cold  bands  of  the  solar  spectrum  to  3//  are  due  to  water,  103-104 

Discovery  of  six  infra-red  absorption-bands  between  11/u  and  18//,  due  to  water-vapor,  by  Rubens 

and  Aschkinass,  in  1898 ... 104 

ABSORPTION  OF  RADIATION  BY  CARBON  DIOXIDE 105 

Knut  Angstrom's  estimate  of  the  absorption  of  solar  rays 105 

Keeler's  measurement  of  absorption  of  Bunsen  flame  radiation , 105 

Relative  radiation  of  HiO  and  COj  in  the  Bunsen  flame 106 

Absolute  discontinuity  of  the  spectrum  of  CO-  (Paschen) 106 

CO2  bands  discovered  by  Knut  Angstrom . . . . , 106 

CO2  band  at  14.7/*  discovered  by  Rubens  and  Aschkinass 106 

Absorption  by  CO2  of  radiation  from  sources  of  different  temperatures  (Tyndall) 107 

APPLICATION  OF  THE  FOREGOING  STUDY  OF  GASEOUS  ABSORPTION  TO  THE  RESULTS  OF  LABORATORY 

EXPERIMENTS ...  - 107 

Curve  of  absorption  of  lampblack  radiation  by  CO2,  derived  from  Tyndall 's  measures 108 

Approximate  curve  of  self-absorption  of  CO2  radiation,  derived  from  Tyndall's  measures 109 

Corrected  radiations  of  CO2  and  of  air  obtained  in  this  research  by  Method  C 109 

Verification  of  Tyndall's  surmise  as  to  the  origin  of  a  residual  deflection 110 

Corrected  value  of  steam  radiation  (Method  C)  ...   Ill 

Corrected  percentage  radiations  from  different  depths  of  CO2  and  air.. Ill 

Concluded  absolute  values  of  radiation  from  pure  air  and  from  carbon  dioxide  at  temperatures  below 

100°  C.  and  with  depths  varying  between  2i  and  125  cm 112 

Comparison  with  previous  results  of  Maurer  and  of  Hutchins  for  air  _ 112 

Question  of  the  probable  spectral  region  in  which  the  radiation  of  pure  air  resides 112-113 

GENERAL  APPLICATION  OF  THE  PRECEDING  STUDIES  OF  ABSORPTION  AND  RADIATION  TO  THE  PROBLEMS 

OF  ATMOSPHERIC  RADIATION 113 

Probable  existence  of  different  types  of  gaseous  radiation,  corresponding  to  varieties  of  spectral  struc- 
ture  114 

Rates  of  increase  of  emission-bands  from  CO2  and  H2O  with  rising  temperature,  derived  from  the  spec- 
tral energy-curves  published  by  Paschen 115 

Approximate  coincidence  of  this  rate  and  also  of  the  absolute  intensity  at  the  maximum  of  the  chief 

COi  band  with  the  corresponding  quantities  for  lampblack  (Paschen ) ...       116 

Evershed's  observation  of  continuous  visible  emission-spectra  from  highly  colored  gases  which  give 

linear  absorption-spectra 116 

Conditions  favoring  the  production  of  radiations  giving  line-spectra 116 

Hypotheses  concerning  the  mechanism  of  radiant  emission 116-117 

ATMOSPHERIC  DUST 118 

Tyndall's  imitation  of  sky  phenomena  by  means  of  fine  particles 118 

Rayleigh's  molecular  diffraction  theory  of  sky  color. 118-119 

Cornu's  observation  of  an  ultra-violet  limit  of  the  solar  spectrum  dependent  on  barometric  pressure  ..      119 
Whymper's  observation  of  brilliant  sky  colors  from  volcanic  dust  ..  119 


134 

Page. 

SUMMARY 119 

Various  origins  and  complexity  of  atmospheric  radiant  emission 120 

Wave-lengths  and  intensities  of  infra-red  cold  bands  in  the  solar  spectrum  (to  4.15/0,  mainly  due  to 

telluric  atmospheric  absorption,  derived  from  Langley's  holographs 121-122 

Approximate  spectral  energy-curve  of  air  radiation  inferred  from  a  combination  of  the  spectral  energy- 
curve  for  a  black  solid  with  measurements  of  positions  and  absorptions  at  band-centers 122 

Estimate  of  solar  radiant  energy  absorbed  by  the  Earth's  atmosphere  at  different  levels 123 

Clayton's  observations  of  diurnal  temperature-range  at  different  levels  in  the  lower  atmosphere 123 

Chief  telluric  absorption- bands  between  0  and  2Qju ,  and  their  intensities 124 

Seasonal,  regional,  and  altitudinal  effects  of  atmospheric  absorption  upon  the  power  of  solar  radiation  125 
Differential  transmission  of  solar  and  terrestrial  radiation  by  aqueous  vapor  and  carbon  dioxide,  and 

the  seasonal  and  diurnal  thermal  effects  depending  on  variation  of  atmospheric  moisture 126 

Wave-lengths  of  maxima  in  terrestrial  spectral  energy-curves  by  Paschen's  law 126 

Dependence  of  terrestrial  surface  temperature-range  upon  relative  humidity  and  this  upon  molecular 

complexity  of  water-vapor 127 

Loss  of  heat  from  the  atmosphere  by  radiation  dependent  upon  transfer  through  successive  sets  of 

molecules 127 

Test  of  possibility  of  radiation  to  the  Earth's  surface  from  upper  warm  layers  of  airs  by  the  phenomena 

of  recovery  from  cold  waves. 128 

Immediate  atmospheric  radiation  confined  to  shallow  layers 129 

Cooling  by  radiation  in  uper  air  (in  addition  to  cooling  of  ascending  currents  by  expansion)  effectually 

lowers  the  temperature  and  prevents  kinetic  escape  of  air  molecules 129 

The  fineness  of  the  solar  chromospheric  spectral  lines  a  demonstration  that  only  the  outer  chromospheric 

layers  of  a  given  substance  radiate 130 

Confinement  of  immediate  gaseous  radiation  to  small  depths  limits  the  loss  of  heat  by  large  masses  of 

heated  gas  and  increases  the  protective  power  of  the  Earth's  atmosphere  against  sudden  loss  of  heat.       130 

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